integral of x^2/(xsin(x)+cos(x))^2

[@punkrockrules205]

tan(x - arctan(x)) + C 1. divide top and bottom by x² so we get 1/(sinx + 1/x * cosx)^2 2. factor out sqrt(1/x^2 + 1) inside the square to get (x^2/(1 + x^2)) * (1/(sinx*1/ sqrt(1/x^2 + 1) + cosx*(1/x)/sqrt(1/x^2 + 1))^2 3. use the formula for cos(a + b) to get (x^2/(1 + x^2)) * sec^2(x - arctan(x)) 4. let u = x - arctan(x) so that x^2/(1 + x^2) dx = du, so that the integral becomes integral sec^2 u du 5. Integrate to get tan(x - arctan(x))

[@blackpenredpen]

WOW!!!!!

[@Folylolyboyz]

@@blackpenredpen sorry I am late but can you explain 3rd line please?

[@shubham-sc3jn]

@FolyPlays Expand cos(x-arctan(x)) using cos(a-b)=cosacosb+sinasinb, use cos(arctan(x))=1/sqrt(1+x^2)=1/x*1/(sqrt(1+1/x^2)) and sin(arctan(x))=x/sqrt(1+x^2)=1/sqrt(1/x^2+1)

[@appybane8481]

@@Folylolyboyz cos(a+b)=cosa cosb-sina sinb

[@tfg601]

@@appybane8481 he knows that ofc he's talking about the line not the formula

[@devprakash5320]

We barely get 2 or 3 minutes to solve this problem during exam So it gets complicated to think like that

[@ohyeahyeahyeah8396]

When you have already done it is easy

[@hammer.11011]

@@ohyeahyeahyeah8396 try solving those 18 questions in an hour and get them all correct 🙂

[@ohyeahyeahyeah8396]

@@hammer.11011 Bhai, mene bhi mains diya hai. Meri 99.2 percentile hai so pls mujhe pata hai kaise karte hai

[@hammer.11011]

@@ohyeahyeahyeah8396 advance ki baat kar Raha hu :)

[@awesomevid5447]

@@hammer.11011 ye 12th class lvl ka question ha bhai.

[@ankit4249]

wow he solves it in 12 minutes but gives us only 2 seconds to try it.

[@blackpenredpen]

hahaha : )))

[@sawmill6358]

You're supposed to pause the video and try it on your own ~

[@adel6019]

@@sawmill6358 It's a joke bro

[@robertpatil6857]

He has to explain it too...😐😐

[@generalginger7804]

pause!

[@saurabhparate]

90% of views on this video will be from India!

[@kawawashaibu6854]

Am from Tanzania

[@satviksharma1146]

From india

[@yugalkishore8991]

I'm IIT JEE aspirent

[@pbraju123456]

True

[@ajmalpuzhakkool4029]

I am from india

[@MoonLight-sw6pc]

He never forgets + c . Quite impressive .

[@bixstar1469]

i ALWAYS forget it

[@TechFabLab]

My auto correct always adds it

[@midhun.m4963]

😂😂😂

[@dqrksun]

EXTREMELY impressive

[@ryancantpvp]

@@dqrksun yo.

[@GaryTugan]

Love these! Your explanations and way of explaining always help me to see clearly the logic and process. So much so that I was able to write the integral down and do it myself from scratch... all the way thru without looking for a hint. And I finished it in around 11 mins. awesome ! Thanks! I find these integrals strangely soothing... :)

[@blackpenredpen]

Thank you!! : ))))

[@leonardobarrera2816]

@@blackpenredpen Do you remember when he was kind with us?

[@ethanpfeiffer7403]

Sure, put it on the exam and hope your students forget about this vodeo/never find it.

[@blackpenredpen]

Yay

[@holyshit922]

Put on exam integral that i found Int(x/sqrt(e^{x}+(x+2)^2)dx) because integral you found is quite easy Wolfram alpha will not help the students and may lead to wrong conclusions Integral which i found can be calculated using tricks like adding zero and multiplying by one \ then apply linearity and first will be easy and for second will be easy to find suitable substitution Int(x/sqrt(e^{x}+(x+2)^2)dx) = Int((1+(x/sqrt(e^{x}+(x+2)^2)-1))dx)= Int((1+(x-sqrt(e^{x}+(x+2)^2))/sqrt(e^{x}+(x+2)^2))dx)= Int(dx)+Int((x-sqrt(e^{x}+(x+2)))/sqrt(e^{x}+(x+2)^2)dx)= Int(dx)+Int(1/(x+2+sqrt(e^{x}+(x+2)^2))(x+2+sqrt(e^{x}+(x+2)^2)(x-sqrt(e^{x}+(x+2)^2))/sqrt(e^{x}+(x+2)^2))dx) If we multiply the numerator we will notice that numerator is constant multiple of denominator

[@yogicbhardwaj7788]

blackpenredpen plz solve this question integral of (xsinx)cosx/sinx + cosx

[@joshuamason2227]

@@holyshit922 calm down satan

[@okgfwij]

What about int(1/sqrt(x^2+1)) 😁 and without using a formula for int(csc(x))...

[@skwbusaidi]

You can write xsinx + cosx as one trig xsinx + cos x = sqrt(x^2+1) cos (x - arctan(x)) Intgeral of (x^2)/(x2+1) × sec^2 ( x-arctanx) dx Let u = x-arctan(x) du = (x^2)/(x2+1) dx Integera of sec^2 (u) du Answer tan ( x-arctan x ) + C If you want to get the same answer , you can use the angle difference for tan. Then, replace tanx with sinx/ cosx

[@divysaraswat2084]

u can also do this ques with substitution : x = tan t... in denominator u can get the formula of cos ( A-B) and with another sub after it we can get the answer

[@Goku17yen]

Lol, one of my friend ask me the Chinese WiFi problem and I answer immediately pi lolol

[@blackpenredpen]

LOL

[@nithin1729s]

Lol

[@ShadicgunMan]

How many digits though?

[@sushilkumarlohani6709]

Lol

[@sushilkumarlohani6709]

@@ShadicgunMan 6-7 maybe doesn't matter you can solve using 355/113

[@quahntasy]

Impossible? Not with blackpenredpen around.

[@holyshit922]

Actually i calculated it as response of RADHA KUMARI comment two months before blackpenredpen I had done it in the same way blackpenredpen did Here we had luck that our numerator cancelled with denominator and we got easy to calculate inegral I think that my above example is worth to record video on it because programs like Wolfram alpha have problems to calculate it and my way to calculate it may be lost in the other comments

[@palashagrawal1551]

@@holyshit922 integration like this are built up to be cancelled out by ILATE method to integrate further .its not by luck .its the design of such question.thats y integration cannot be done by framing questions ourself ..

[@decentman7555]

kzbin.info/www/bejne/r5C7qIShmM2qqKc

[@anubhavverma2297]

This is possible. and Title is not correct. I have solved this with various methods.

[@vineet5322]

i did this same problem at my preparation time, really good question to practice . i think the better way to do this is by writing x(square) on numerator as x(square)[sin(square)x + cos(square)x ] and then solve for it ,i hope it will help you.(it is little bit complex approach but it will open your mind) or anyways you can always use any suitable method feeling comfortable with.

[@gouravpandey3513]

How........... What are.. The next steps

[@bukler3934]

Honmestly impressed by the clear explanation and the fact that you went over all the passages. Also really great attitude

[@alephnull4044]

Very cool, and it's great that you explain exactly how you come up with each step. Many teachers don't understand that showing how you think of the solution in the first place is more important than the solution itself.

[@TheBlueboyRuhan]

Can't wait to slide this to my friend as an easy "Calc. 1" question #YAY

[@ankushsingh4614]

Sir Rahmed what is calculus 1?

[@OtherTheDave]

Ankush Singh The first calculus class. Where I took it, “Calc 1” covered derivatives, “Calc 2” was about integration, and “Calc 3” - sometimes called “Multivariable Calculus” - was about applying Calc 1 _and_ Calc 2 to situations involving more than one variable. AFAIK, they’re broken up somewhat similarly across the country (USA for me, dunno about Sir Rahmed) so that it’ll be easier if you need to switch schools. Within reason, of course... you can’t translate classes from a school that uses semesters (about 4 months) to a school that uses quarters (3 months), for example.

[@Capnarchie]

Sir Rahmed guess who I found scrolling on the interwebs

[@TheBlueboyRuhan]

@@Capnarchie No way, you watch blackpenredpen too? ;)

[@Capnarchie]

Sir Rahmed sometimes

[@holyshit922]

Maybe some people dislike this video because division by cosx changes the domain To use another choice for parts we need to manipulate the numerator for example multiply numerator by one (pythagorean) and add zero to be able to use linearity in the way that in first integral numerator cancels with denominator and second can be integraten by parts but with different choice of parts

[@kingbeauregard]

I say those are magic pens that know how to do calculus. I want those pens.

[@mathonthego1947]

"Let's do some math for fun" Ummm, don't we always do math for fun?

[@blackpenredpen]

Math On The Go totally!!!

[@decentman7555]

kzbin.info/www/bejne/r5C7qIShmM2qqKc

[@pranavbharadwaj521]

As a 12th grader studying in India, I can say without a doubt that questions like this are the ones you should be skipping 😂

[@decentman7555]

kzbin.info/www/bejne/r5C7qIShmM2qqKc

[@friedsugar2701]

Kyu?

[@Kkaran8404]

Time jayeega. Simpler ones pehle karlo

[@akshatsaini69]

haha, this is an ncert exemplar question btw💀😭

[@VBM375]

​@@akshatsaini69 it is definitely advanced level

[@pwootjuhs]

6:19 bprp: so, we're gonna stop right here... youtube: *An error occured, please try again later*

[@marlonbrade9424]

I hope my sister will not find your video. 😂😂😂 I will give this as her exercise 😏😏😏.

[@blackpenredpen]

marlon brade lol, nice!!

[@DonutKop]

Thanks for reminding me to subscribe. I had been watching your channel for months and just completely assumed that I had subscribed to you already because I watch your videos so frequently!

[@blackpenredpen]

DonutKop awww thank you!!!

[@tomatrix7525]

I love how his writing gets quicker and more figidty as he approaches his solution. You can see the excitement building! Also, very clever manipulation to be able to intgerate by parts!!!

[@Hexanitrobenzene]

Integration by parts for quotient. Damn. Clever.

[@blackpenredpen]

Yay!!

[@sauravmnsingh4532]

It doesn't sound good. May be you get the answer .

[@chinisa.innukshopa]

LIATE (logarithm-inverse trig-algebraic-trig-exponential): a powerful tool but not always the best

[@tushargahlaut5812]

We were taught ILATE instead of LIATE.

[@shayanshaikh534]

Isn't it ILATE and not LIATE

[@chinisa.innukshopa]

Maybe, if you don't mind sounding like the White Rabbit from Alice in Wonderland (-; one pill makes you larger.... ;-)

[@abhinavtiwari6438]

It's ILATE

[@shashwatjohri1503]

we are taught ilate .

[@MrLuigiBean1]

Gosh, I love that moment when I'm riding along with the explanation and suddenly something clicks into place! Awesome video!

[@nuduw]

I actually solved it by dividing the numerator & denominator by (cosx)^2. Btw, this question was asked in our weekend exam. I'm taking the IIT-JEE exam on May-19-2019.

[@karteke]

How did it go?

[@sidharths2355]

How did you simplify

[@decentman7555]

kzbin.info/www/bejne/r5C7qIShmM2qqKc

[@voidmain7954]

are you alive?

[@nuduw]

@@karteke Failed to clear the chemistry part ;-;

[@adi-xd8ze]

These type of questions come in jee advanced exm which have to be done in 3 to 4 min and this was an easy one. Keep up the good work

[@qwertyuiop2161]

easy if you know the trick.

[@nalin8050]

We did this problem in the 12th class, so... Of course,I'm from India.

[@julu2731]

we got the india part from your name.

[@nalin8050]

@@julu2731 so funny hahahahaha. Stfu

[@nalin8050]

@@julu2731 it's because I liked that game called king of thieves very much.

[@ja.m4947]

Yeh this question was for CBSE board eaxm 😂😂 I wonder why he even categorised this question for JEE prep 😂 like what a mockery this is

[@jeshurunluke5573]

Come on man I did it in my 10th grade, and I am from the US. Pretty sad you only started it in your 12th.

[@holdenh-dawg8772]

It’s only impossible when more than two pens are required

[@decentman7555]

kzbin.info/www/bejne/r5C7qIShmM2qqKc

[@田中_田中]

Since the order of the denominator of ○'/○^n decreases and becomes simpler when integrated, it may work well to use it as the integrating side of a partial integration.

[@dhruvvraghu6226]

Apparently everybody is an integration champ from MIT here.. If you wanna boast go somewhere else, this is for the ones who wanna learn.

[@caravan1996]

Yeah you are right.

[@banana6108]

Yes

[@msk4246]

THESE QUESTIONS ARE SUPPOSED TO BE DONE IN 3 4 MINUTES AND WITH THE PRESSURE THAT YOUR FUTURE SOMEWHERE DEPENDS ON THEM... THAT'S WHY NO EXAM CAN BEAT JEE ADVANCE IN TOUGHNESS

[@blackpenredpen]

😮

[@raghav9o9]

Lol look at KVPY it have the most hardest problem in mathematics which are based on not your mathematical skills but how is your scientific approach to mathematics. Also JEE advance is nothing in front of KVPY

[@msk4246]

@@raghav9o9 KVPY IS TOO EASY LOOK AT IMO PUTNAM BRO.... BTW I'M IN 10 AND PREPARING FOR JEE AND IMO....

[@raghav9o9]

@@msk4246 bro comparing jee it is harder and try to solve question of kvpy also we don't have to fight on this matter we are humans we are here to solve problems not to tell which one is harder every exam has its own level.

[@raghav9o9]

@@msk4246 I know putnam is very hard I didn't even try its problem I love mathematics because it tells about the beauty of nature not to pass an exam so stay blessed.

[@golammartuzahossain6748]

I've found out a more inquisitive way to solve it. use harmonic addition theorem on the denominator,and take the argument of the sine function(or cosine,depending on which one you prefer to use) as u,and differentiate.Also you'll have to to an easy partial fraction which immediately follows. Just try it!

[@holyshit922]

Harmonic addition ? Is it possible ? Coefficients in front of trig functions are not constant

[@golammartuzahossain6748]

Doesn't necessarily have to have constant coefficients. try to write the denominator as sin(x+arctan(1/x)) then take the argument of this sine function as u and see what happens

[@pco246]

How would you even think about that? OMG

[@golammartuzahossain6748]

Well the denominator looked that much tempting to me to use the harmonic addition PCreeper

[@kunwarshaanjeetsinghgrover2102]

That thoerom is not in the syllabus of the exam i think. But if its a good method then good for you!

[@person1082]

bprp: It’s actually pretty easy. You just start with a quotient, you differentiate that, and if you see a lot of simplifications it will make the integral really really hard. me: the derivative of sin(x)/cos(x) simplifies all the way to sec^2(x), therefore it’s really hard

[@Barman1904]

Another easy way can be by dividing Nr and Dr with 1+x² This will create a sin(x+A) form where sin A = 1/√(1+x²) Then put x+sin-¹(1/√(1+x²)) = t dt= x²/(1+x²) dx Simple

[@fengshengqin6993]

Hi ,thanks for clearly integral by part. I didn't get this way to integral . I changed xsinx +cosx=cos[x-arctanx] (x^2+1)^(1/2) then this integral has been transformed into X^2/(X^2+1) times sec^2[x-arctanx] ,then I found that d[x-acrtanx]=x^2/(x^2+1) , So I used U substitution , then result is tan(x-arctanx) , I think this is more clear than the wolfram alpha's result .

[@venkatbabu186]

X sqared means a regular square pattern. Xsinx means multiple waves. cosX added means inverted angles or I. Squaring multiple waves and Angeles ninety means absolute values of waves instances. When you divide one by the other and integrate you get circular ripples.

[@Quwertyn007]

Whenever I see this exam's name all I can think is YEET

[@abhirajarora7631]

Yeah, students get yeeted every year. I am about to be part of that tradition in two days.

[@manhwamaniac21]

If we add plus n(n-1) in numerator and n as the coefficient of cosx in denominator it will have a general solution of ( -xsecx/xsinx +ncosx ) +tanx +C Here in the question n is equal to one.😊😊😊 Hope it helps ciao

[@mitsu7june]

How?

[@progamersfire1573]

Ye sawal 2 ghante me nai bana ..DOUBTNUT NE BHI NAI BATAYA🤣ACHANAK MIL HI GAYAA

[@theT3901]

Wah

[@craftbuzzwonky4752]

🤣🤣🤣🤣

[@by7212]

The way you approach problems help me with my maths mainly integrals.

[@bharatsoni9577]

our teacher did this with 3 methods Anna Sir

[@mariakhan6090]

yes! Anna sir!

[@Nasir.365]

Sab batana hai is BHARAT ko, xD!

[@rengokukyojuro1384]

as someone preparing for jee i remember this question as a format of forcing by parts. it was really long but satisfying.

[@x-warrior8517]

that was great explanation.thank you

[@skwbusaidi]

My answer is tan ( x-arctan(x)) + c I hot this by converting the denominator to one cos And this is the same answer if you use the formula for tan the diffrence between two angles and then convert tan to sin/cos

[@coolnig7124]

This is not even a JEE level question. Even someone like me who is not preparing for JEE can solve this. JEE questions are much harder than this

[@biswadevmajhi231]

I have solved many jee question but this one is tough

[@allipse8224]

@@biswadevmajhi231 for advance, it's moderate level

[@nathanielhensley4830]

@@allipse8224 Can you just stop?

[@ichigo449]

@@nathanielhensley4830 It's like the Gaokao or Oxbridge Entrance Exams. Students study specifically for these tests and attend cram schools for years.

[@nathanielhensley4830]

@@ichigo449 I know what it is. It's nothing to be proud of.

[@madalina-laviniadulhac1764]

Watching you is much better than social media tho

[@OonHan]

Here is my solution: wolfram alpha the integral. DONE

[@blackpenredpen]

Oon Han yay!!!

[@rrr1304]

Not in jee syllabus

[@Nobody-pv9jt]

@@rrr1304 dude issa joke

[@pureaura4608]

For integrating by parts try this FIS-DFIS (FIRST*INTEGRAL OF SECOND) MINUS (INTEGRAL(DERIVATIVE OF FIRST*INTEGRAL OF SECOND dx))

[@_AmbujJaiswal]

This question came recently in jee main exam which is an entrance exam to just sit in IIT jee exam🙂

[@zynade9334]

Which shift?

[@_AmbujJaiswal]

@@zynade9334 bro this is forcing integration by parts method I am not sure which shift but it was in 2020 spetember attempt🙂 (Or january not sure but it was in 2020 mains exam)

[@zynade9334]

@@_AmbujJaiswal Ok thanks, I found it

[@explorer4459]

I think similar problem is in grb calculus book and I did it by assuming that answer is f(x)/xsin(x)+cos(x).and differentiating and equating it to the original expression.it was then easy to predict what f(x) could be

[@brittoaugustus4060]

I did this problem using the ''Harmonic addition theorem'' and I got a slightly different answer.

[@orient9439]

THE WAY U TEACH MAKES THE SUM APPEAR EASY SIR YOU ARE SUPER AWESOME

[@paultoutounji3582]

Love the integral and enjoy your way of teaching ! Always a pleasure to watch and listen ! But this intergral should not be in your calculus 2 EXAM but in a homework that could be evaluated . :D

[@williamkrueger268]

Yes, great exam question! I came up with a different approach, but this was an easier way to arrive at the solution.

[@dottorgelo292]

Hi Bprp, I wanted to buy two of your “derivatives for you” T-shirt, but I’ve just noticed that the campaign on Teespring.com has ended two days ago, is it correct? What can I do? Thank you a lot, you’re awesome!

[@blackpenredpen]

Hi Dottor Gelo, Yea, it has ended, but I might put it back on again. I am just working somethings out with them at the moment. Sorry.

[@dhruvgupta7046]

I was new to your channel, so I asked you to try JEE. But you actually did it way before... You are awesome bruhh

[@SartajKhan-jg3nz]

Yeah give it in your Calc 2 exam and dont forget to post the students' reaction!!

[@blackpenredpen]

: )

[@danbarsan6936]

donitzeti

[@anuraagrapaka2385]

#ChallengeToBlackpenRedpen Integrate 0 to x floor(t+1)^3 dt Where x belongs to positive real number set

[@anuraagrapaka2385]

----Floor function also referred to as Greatest Integer Function

[@n0lain]

I'm not gonna lie, I'd probably have missed this question if it was on my calc 2 exam lol

[@mark_tilltill6664]

Recipe for crazy integrals: 1. Generate some crazy function 2 differentiate it. 3. Slap an i integral around the derivative . 4. Unleash on students. Watch the fun.

[@vikasrawat7999]

U know about IIT ? WOWW

[@chocoice9]

@@dr.mikelitoris no u

[@RC-qi6hs]

@@deviprasad_bal I think it's 3rd most difficult exam

[@deviprasad_bal]

@@RC-qi6hs no it's 5th... 1st-CCIE 2nd-GATE 3rd-Gaokao 4th-UPSC 5th-IIT-JEE

[@RC-qi6hs]

@@deviprasad_bal Ty for d correction

[@ritik5223]

@@deviprasad_bal lol out of top 5 difficult Exam 3 exam are of india

[@swastiksahu1312]

You could also expand the numerator to x^2sin^2x + x^2cos^2x and simplify.

[@gautamwadhwani2033]

I read the description that it was by parts and solved it easily!

[@parthsingh3057]

Another way from 2021 :) Bring the numerator to 1 via dividing by x^2, and compress the expression in the denominator via trigonometry. You should get ( x^2 * cosec^2( tan-1(1/x)+x ) ) / (x^2 + 1). Then you can directly substitute for tan-1(1/x)+x = u, and get the solution. Btw, when I saw this the first time, I didn't see that the denominator had a whole square lol. Lemme know if I missed something, though I hope I haven't.

[@rimanbachar7588]

Thanks for helping.🙏 Love you💖💖💖💖. 👍👍👍👍👍👍👍👍

[@protoword10]

I just suscribe to this channel, it brings me memory of my college years...👌

[@Archipelago.]

Famous problem of JEE ...😂😂 Everyone can solve it Jee preparators raise their hands from crowd 😂🤣

[@lordx4641]

This was a class 12 problem

[@anjulhariharce-3192]

🙌

[@phythematics2188]

RD Sharma Volume 2 Page 19.132 Example 14

[@decentman7555]

kzbin.info/www/bejne/r5C7qIShmM2qqKc

[@ashishgiri2373]

Even i have been taught this by my teachers but this explaination cleared my concept thnks sir

[@pooydragon5398]

Great video. Could you please make some videos about teaching some methods instead of explaining problems. That would really help me! Thanks

[@muhammedg-tips1584]

Bro you make it a piece of cake great effort here ♥

[@chimetimepaprika]

This made me unsubscribe just so I could resubscribe for emphasis.

[@blackpenredpen]

chimetimepaprika Hahahaha aww thank you!

[@peeper2070]

I was about to try it until I realised it was integrating not differentiating. Not at that stage yet but I’ll be sure to come back in 12 months when I learn it.

[@chandanverma6523]

It's good w Question.... I'm from Varanasi India

[@Subro_Plays]

I never thought that this could be done so smartly

[@kushagrapandey2466]

Thanks sir I'm an JEE aspirant. My exam is on 2019.❤Thanks for the video, I'm studying at 3:00 AM this came in my recommendation and helped a lot. Btw which country are you from?

[@kushagrapandey2466]

@Sashank Sriram not every asian is chinese bro.😂He can be from Philippines, korea, japan, Vietnam

[@HitmanReborn9999]

@@kushagrapandey2466 ...That doesn't mean he's not Chinese though?

[@holyshit922]

Here we can build differential equation from this result df/dx (xsin(x)+cos(x))-f(x)xcos(x)=x^2

[@manjushasonar6701]

My jee exam is on 9 Jan 2019

[@amj.composer]

Wonderful method sir! So much easier and "obvious" once you know the solution (if that made sense) Thanks for the video. I'mma use this method.

[@prahladgurjar9700]

Damn ! If this was the question the question in last year's cbse board, 80% students of India would've got full marks in this one. 😛

[@praveensingh4525]

Stop exaggeratating. Boards have way more easier problems. :)

[@laffus]

thank you man, for you i'll pass my examen

[@mayankraghuvanshi3393]

I have my IIT JEE exam on January next year 🤪🤪

[@TheRayll]

good luck

[@TheRayll]

it's jee mains? yea?

[@mayankraghuvanshi3393]

@@TheRayll yes it's JEE mains

[@mayankraghuvanshi3393]

@@TheRayll thanks a lot

[@mayankraghuvanshi3393]

@Rahul Pavan yes bro,but widely people know IIT JEE

[@JokerAndEverything]

I felt this was more of a guess and differentiate question rather than integrate. d(u/v)/dx= (v*du-u*dv)/u^2. Now if you'd notice the denominator is in terms of square. Rest of it is just finding v and v' which can be guessed with not too much efforts. If you want to call it a scam of a solution, its alright but this gets stuff done fast which is required. Disclaimer: You get to develop the intuition for the method only by practicing hard. So current JEE students should practice more as compared to cheats like this.

[@chandrabitpal9151]

Actually this is one of the easier integrations of iitjee sometimes they ask national mathematics Olympiad level problem those are the main crunch these are the bonus questions that iitians clear

[@donaldflynn8300]

Huh - I did it by writing it as x^2/[(x^2 + 1)(cos^2(x - arctan(x))] (using Rcos(x - alpha)) which= [1 - 1/(x^2+1)]sec^2(x - arctan(x)) and then the substitution u = x - arctanx works. I definitely prefer your method

[@TejasKd221B]

So its not impossible, ISN'T IT?

[@decentman7555]

kzbin.info/www/bejne/r5C7qIShmM2qqKc

[@alterrainbow9478]

I’m only 16, I think we raise every factor inside the parentheses which will then be the indefinite integral of x squared over x squared times the square of sine x plus the square of cosine x. Sin^2(x) + cos^2(x) = 1, so the equation becomes: x^2 / x^2 * 1, any number multiplied by one stays the same. The equation becomes the indefinite integral of x squared over x squared and then the indefinite integral of 1 dx which results in x plus the integration constant. x + C We don’t learn about calculus yet, so this could be horribly wrong and stupid.

[@nme7885]

This is basic RD sharma math

[@amj.composer]

Nonsense. Sab ne maths padha hai show-off ke bacche. Basic nahi hai, advanced hi hai.

[@abhig7622]

@@amj.composer true😂😂

[@Nitro-kx7ok]

@@amj.composer Kon de class me hai Bhai chota hai Kya 12 me ncert dhang see Ni kri na????

[@amj.composer]

@@Nitro-kx7ok Bhai, hindi nahi aati? Thoda dhang se likhne ki koshish kar. Tere spellings ko dekhke lagta hai ki na tereko English aati hai aur na maa baap ne Hindi sikhayi.

[@animalfarm7467]

This is the question one would use in a multiple selection. For example, four of the following six questions must be completed to complete the exam. Let them select this question at their own risk. They need to learn early; not understanding their limitations and bad choices have consequences.

[@prathmeshchhabra2010]

Khosa.... X (cosx)

[@bruhmoment1835]

Dammit cosine x

[@jarikosonen4079]

To find the right integration method looks most difficult. But this seems maybe the best here.

[@mariakhan6090]

This is so famous and becomes a cakewalk with two substitutions that my teacher pointed out: x=tan θ and then (tan θ - θ) = t you'll get the answer straightway

[@erickherrerapena8981]

No lo habia pensado de esa manera. ¡¡Buen video!!

[@AndDiracisHisProphet]

you are way to little of a meaniepus to put this into your exam^^

[@blackpenredpen]

: )

[@vivektiwari1873]

Your pronunciation is literally amazing.

[@imgaurav7627]

This is not that tough. I asked this question to all of my friends. They were able to do. Btw I too had cracked JEE Advanced with a rank of 9712 and got admission in Indian Institute of Petroleum and Energy (IIPE), Visakhapatnam.

[@blackpenredpen]

im gaurav good for you!

[@imgaurav7627]

@@blackpenredpen A good reply sir!! But I wasn't trying to show off or anything like that. I just meant this question is okay but not that tough to be called impossible. Btw you are doing a great work by providing education. I really appreciate it!!

[@blackpenredpen]

im gaurav well, I put "impossible?" Since I think people would be wondering if that's even possible or not in the first place. So yea.

[@imgaurav7627]

@@blackpenredpen Ok. I got it. Still 'good for you' was a bit rude. It doesn't suit to the educators like you. And going through all you content, I must say nice work man!

[@hemant4mech]

You were trying to show off. Your rank in Jee Advanced cues that it is highly improbable for you to solve such question in first try unless you are familiar with it.

[@brotabanerjeetripathi2410]

Me: yet another video of BLACKPENREDPEN Me (After watching 1:00 ) : Ohh wait it is BLACKPENBLUEPEN

[@ggodfather]

We have a similar question in our Maths book(Cengage) Only diffn is that in the numerator its x2+20 And its even more tricky!

[@tapasyogi7931]

Put x=tan y and things become much easier..and faster