integral of x*e^(2x)/(1+2x)^2, LIATE DOESN'T WORK HERE

integral of x*e^(2x)/(1+2x)^2,
integration by parts,
integration with DI method,
hard integration by parts,
calculus 2 integral examples,
DI method,
www.blackpenredpen.com

[@Jonathan-rf5cp]

"And the integral of this is...782 dollars!!!!!" - youtube ads have great timing

[@ToonZIndia]

where to put the ads is chosen by the creators

[@gravnine]

@@ToonZIndia sometimes KZbin ignores the timings put in by creators and ads play at random moments

[@sansamman4619]

I think the category should be: entertainment...

[@blackpenredpen]

lol yea!

[@MigligM]

Just here to say thanks from Brazil, just passed my calculus 2 exam! You're a great teacher and it's nice that you're solving all this different integrals on your channel, usualy we can only find the methods and simple examples on other channels, its awesome that we can get so much more practice on all the extra examples you're solving! I also dig how you smile at the camera from time to time, we get to see your passion for math and it kinda makes more bearable to learn from it, i already finished all my calculus 2 exams but im still here watching you, and i kinda hated calculus with all my might before lol. Keep killing it! Peace!

[@blackpenredpen]

Hi Miguel, Thank you for your nice comment! I am glad that my videos have been help you! Keep up with you good work in your classes! bprp

[@jjtt]

*whitechalkredchalk

[@factsheet4930]

Rip pens

[@anjelpatel36]

Yaayyy...

[@Simon-bl9wk]

realy sympathetic teacher.. Thank you! Greetings from Germany

[@blackpenredpen]

You're welcome!!

[@diegojesusduenascollado7043]

@@blackpenredpen Hi, isn't it possible that the second part of the integration can be integrated as arctg(2x)??? (1/1+(2x)²)

[@coderanger7708]

@@diegojesusduenascollado7043 that's not possible as we need it to be x^2 and not 4x^2, even if you try to take u = 4x^2, remember that to go to U world you have to differentiate u and write DX in terms of du, on doing that it'll change how the integral looks.

[@zzwag]

BPRP your channel is growing so much!!! Congrats! Also, I ended with an A in Differential Equations last semester thanks to you! Again thanks so much. This fall I'm taking linear algebra :)

[@blackpenredpen]

zZwag that's great! Keep up with the good work!

[@gregoriousmaths266]

zZwag I tried for like a minute to get that fly in ur pfp off of my screen lmao

[@jalenjackson8572]

This dude is so good at teaching this stuff. My teacher is in no way a bad teacher, just seeing how someone else does it is so helpful.

[@KaKam0u]

At 0:35 you say it can't be done by u substitution, but u = 1+2x works too and I found it simpler that way. It doesn't avoid having to do integral par parts though so it doesn't really save much time in the end.

[@TechnoSan09]

Yes then it'd become in the form e^x(f(x)+f'(x)) which is e^x. f(x) +C

[@jeremyclark4992]

Thank you so much for posting your videos. They have helped me tremendously as I'm sure they have many many others.

[@Edenchungkhoan]

I have a tendency to "open math problems" like this. When I solve them already, I go online, look for other better way for them to learn extra procedure. In this particular problem, this remarkable professor and I have the same way. And I'm quite sure that is the best way for this problem. :)

[@HimanshuSharma-yw6su]

Alternate method: The derivative of f(x)*(e^g(x)) = (e^g(x))*(g'(x)*f(x)+f'(x)). In this case g(x) = 2x, Hence we need to find f(x) such that 2f(x) + f'(x) = x/(1+2x)^2. By observation, f(x) should be of the form m/(1+2x). Putting this in the equation gives m=1/4. Hence we get the integral as (e^2x)/4(1+2x) + C

[@AriasFco]

Please do some eliptical integrals, I need to refresh them a bit. =)

[@pierrelavry8426]

Francisco Arias )

[@suniltshegaonkar7809]

Integration by partial fraction, dU is -ve and as well Integral V; so the product is positive. But there remains the negative sign from the formulation to take effect. Check at 6:48.

[@dipun4849]

Your solving methods are heart touching.❤️❤️❤️

[@Omar-sq6zz]

Perfect explanation with deep details I appreciate your work.

[@yuvalpaz3752]

great video, in other matter, can you do fourier transform videos like you did with laplace transform?

[@noide1837]

My man, thank you. I could not get past this problem in my homework. I had so many aha moments watching this video, and really every one of your videos that I've watched.

[@itoldyounottotouchit3336]

I love how the chalk colours match your sweater.

[@gabrielpheme6118]

fascinating. the way you flow with your maths. doing it with love. I'm inspired.

[@shanecoyle3676]

Im a first year chem student (i have to do maths for 2 years tho but i love it) this seems like theperfect problem for someone my level chain rule product rule integration by parts and by substitution all used. Its perfect. And tge speed you teach at is perfect for me personally because im pretty comfterble with this. But man this is a perfect vid.

[@yellow-is-my-jam8D]

You are a legend Sir, thank you so much for making these lessons easy to learn and concise. Wish us all luck in our Calc II exams!

[@sansamman4619]

that integral is so beautifully written!

[@tehyonglip9203]

i prefer chalkboard over whiteboard, you can do many crazy things like drawing a circles with protractor and dotted lines with chalkboard, you cant do anything with whiteboard. whitechalkredchalk>blackpenredpen

[@TechnoSan09]

But the particles would get into my nostril And hands will be shabby

[@samiahmed1942]

this man is a living legend. you are the best

[@vedantpatil1095]

Sir, u are awesome, pls can you upload more videos like these type

[@MarkMcDaniel]

Elegant solution for a messy integral.

[@alaba5085]

¡El mejor explicando la solución de Integrales!

[@blackpenredpen]

thanks!!!

[@BeenYT]

you can solve by u sub if u sub in u = 2x+1 which yields ( after inserting x= (u-1)/2 and (2x+1) = u and cancelling everything and taking out the constants) 1/4e integral of ((ue^u-e^u)/u^2) du = integral of (e^u/u) - integral of (e^u/u^2) which is EI(u) - (EI(u)-e^u/u + c) = e^(2x+1)/e*4(1+2x) + c = e^2x/4(1+2x) + c

[@shahimmujteba944]

Complicated question, complicated answer.lots of love from India

[@Metalhammer1993]

"product and quotient rule are the same thing" reminds me of 12th grade. amths teacher got pregnant we just had done product rule new maths teacher thought we were done with the chapter and in the exam was a shitload of fractions we had to derivate. man can you imagine the pain we were in?^^ i mean i for whatever reason remembered middleschool maths. and thouht i can just write the fraction u/v as u*v^-1 and differentiate this. man i was glad it only had simple stuff in the denominator like x^4. everything would have been physical pain without knowing quotient rule^^

[@trueriver1950]

you can use your trick to derive the quotient rule from the product rule if you have more than one quotient to differentiate. I had to do that when I suddenly had a memory failure during an exam.

[@Metalhammer1993]

i know nealry got hit for that from other guys in my semester. first semester chemistry. our prof asked who never heard of the quotient rule^^ some raised thweir hands. "hwo did you derive quotients then?" i said product rule and that guy "that would be a nice task for the exam thanks" we all fucked up^^ please derive the quotient rule from the product rule. i could do it in school but i could not do it correctly in theory in university man that sucked^^

[@gcewing]

I don't bother remembering the quotient rule. Products with negative powers work just as well.

[@che7045]

What you said is really easy to understand . Thx u so much.

[@poncesebastian7875]

This integral came in my exam damn it!

[@marlonhautecoeur34]

thank you so much blackpenredpen

[@antoniocampos9721]

Good. Your example helped me to solve another problem.

[@artrose1717]

What a great teacher you are, thanks for your uploads!

[@blackpenredpen]

Thank you Art!

[@prollysine]

Dear bprp, congratulations on the example, the solution is surprising and fun !

[@blackpenredpen]

Thanks

[@ambikasenapati9947]

We can take e^2x/1+2x = t Differentiating it will give us 4 xe^2x/(1+2x)^2 dx = dt which is basically the question. Its shorter

[@adinovianto1545]

Thanks you so much. Sangat membantu saya

[@reetasingh1679]

If you substitute u=2x+1, the integral reduces a lot, to the point where it breaks into two integrals. If we then use LIATE on the first integral, it eliminates the second integral, making life a LOT easier...

[@osamahafez4548]

Thank you for making our life easier .

[@jamiea.espinozar.7534]

You saved my life 😭❤

[@kimrocha1320]

You can do u-subs to u=1+2x too and separate the substituted equation into a sum of two integrals. Then, u have: I = 1/4e*[int(e^u/u)du - int(e^u/u^2)du**] So, if u apply integration by parts to first integral, taking e^u as dv and 1/u as w u have: int(e^u/u)du = e^u/u - int(-e^u/u^2)du int(e^u/u)du = e^u/u + int(e^u/u^2)du** Now, u can cancel (**). So: I=(1/(4e))(e^u/u)=e^(u-1)/4u = e^(2x)/(4(2x+1)) I think it is the first "blackpenredpen's integral" that i pwned alone, im very proud of that :)) thank you, your channel is awesome!

[@professorjessen]

Good job! Linear substitutions simplification should have been obvious. There’s need to pull out the 1/e though. e^(u-1) is its own derivative and antiderivative, and the backsub is going to be happier when you’re done, too.

[@nationalstudyacademykim5030]

Touche! Nicely Done Sir!!!

[@engr.rimarc.liguan1795]

Sir. Please help me with regards this situation: integral of (-ln x /(1+e^2x)) dx at lower boundary of 0 to the upper boundary of 1. Please investigate this also if it is divergent or convergent. But I really do, it is convergent. But it is really tricky to solve because it cancels out. Thank you.

[@bharathegde5899]

So glad he put the +C in the end!

[@dangerxgaming9475]

Its was the best video that i have wver watched 😊

[@timeonly1401]

Saw 2x in a couple places, along with the single x up top, which can easily be made into 2x by multiplying by 2/2... I let u = 2x => du = 2dx . Subbing & factoring out 1/4, gives a cleaner: (1/4) integral[u e^u (1+u)^(-2) du]. The rest is easy.

[@saxbend]

Why doesn't the minus sign at the beginning of the second row cancel with the -1 in the numerator of the integrated fraction?

[@spixdusk6899]

i love u tnks for your work ^^

[@kaylawagner3295]

Thank you for this video!

[@2kabdul429]

This video helped so much thank you

[@karangarg4631]

I have a small query, at 5:50 when you write the first part of the answer, why is it negative? From the D column, the expression is positive and in the I column is the expression not also positive (because the negative sign in the expression cancels with the negative sign at the start of the second row)?

[@blackpenredpen]

I had a video here explaining what to do in general kzbin.info/www/bejne/aHqQkIaMbciqqdk

[@anitapalvlogs1978]

Very niece explain sir👌👌👌

[@ibanguniverse811]

Hey, I didnt see his lecture, I just saw his cute handsome face

[@Salah-fn]

OMG you are an awesome teacher I love you sir veryyyyyy much❤❤❤❤❤❤❤

[@durgaganesula2981]

Super a little bit tensed the best because of your the fashion on explaining I am a 10th grade student of IIT FOUNDATION

[@user-dd4mr4nv5g]

Hi, before all thank u from the heart, but I have a question could we get the integral by the equation in the top with a negative exponent? in the first step. Because I just solve it by using this way and I had a different answer :(

[@salihabatool4794]

u are extremely fast and wonderfulll......

[@madushanbuddika4585]

Much love from 🇱🇰 ❤️

[@dianamariasantos5482]

este men es un grande wn

[@danieljimenez2725]

What criteria did you use to stop the derivation and integration of the two functions? Everything else made sense but I'm not sure exactly when to stop the integrating and derivating. Great videos btw

[@MrLucky-oq6vq]

We integrate one time

[@diartbajraktari9128]

You atop when it’s 1.easy/easier to integrate 2.you get your original function again

[@holyshit922]

Integral of x^2/(x sin x + cos x)^2, LIATE also seems to not work here but integration by parts works

[@thamkaionn3785]

+blackpenredpen why the DI method notworks for (sec^2 x)(ln(cos(x))?

[@desertrainfrog1691]

White Chalk Red Chalk is my favorite BPRP Variant.

[@joudh.7457]

How did you know to stop after deriving and integrating once? Like don't we keep deriving and integrating?

[@lalitdogra22]

You're perform maths in the best possible way :)

[@davis2018]

i really appreciate this bro!!

[@wristdisabledwriter2893]

I think I saw your previous way because I did it by recognizing that it looked like a quotient so I did it by showing the quotient

[@Dogface1984]

1/(1+2x)^2 can be integrated as arctan(2x) with u=2x

[@sindyluhs8607]

Thank you so much !

[@chaitanyaparanjape7837]

Hey plz tell me if you find this method useful :) I am solved it by using formula Integration { e^x [ f(x) +f'(x) ] .dx } = e^x [f(x)] +c 1. substitute 2x=u & simplify to get NOTE: There is 1/4 outside integration e^u [ u/ ( 1+u )^2] 2. add & subtract 1 in numerator to get it in this form e^u{ [1/(1+u)] + [ -1 / (1+u)^2] } 3.now comparing with formula we get f(x) as 1/(1+u) Therefore ans is obtained just by placing values in places of e^x[f(x)] +c

[@abdikanimusehalane5054]

Thanks, I'm gonna have Calculus 2 exam in one week

[@user-ld7mc3hw6c]

such a great teacher

[@camhongluu4189]

I solve this by factoring the numerator. In the integral, we see the denominator is in the from of “post-quotient rule” differentiation. I put A as the numerator of pre-differentiation, or the numerator of the resulting integral, then apply the quotient rule. Then we have: x.e^2x = A’(1+2x) - 2A Then, A’ -2A =0, and 2xA’ = xe^2x Then we will have A’ = [x(e^2x)]/2 and A = [x(e^2x)]/4 This is just for fun and fast for the math of multiplication question. I know the step and work it “backward”, but put it in proper explanation..kinda no😅

[@yasley444]

THANK YOU SO MUCHHHHHHHHHHHHHHHHHHHHHHHHHHH

[@jeleelphusjabu6068]

How can we get help or ask Questions, please help, if is possible

You are the man!

[@blackpenredpen]

Thanks.

[@jackkalver4644]

I thought of 3 methods myself: this one, integrating x/(2x+1), and expanding the integrand.

[@snbeast9545]

"Prada Rule" Damn, I didn't know fashion was THAT strict!

[@aneedfortheory]

The integration by parts formula is int u dv = uv - int v du, no? So, what happened to the minus before the int v du? I solved the question using substitution and then LIATE finding your answer but with a negative, viz, -e^(2x)/4(1+2x)^2 + C. Great videos btw!

[@Convergant]

question: could you not just set u=e^2x du/dx=e^2x dx=1/e^2xdu since u=e^2x, x=ln(u)/2 and 2x becomes ln(u) to get the integral of ln(u)/2(1+ln(u))^2?

[@user-xi5yz5xs6u]

blackpenredpen's little brother... whitechalkredchalk

[@zelmafiereder]

Love u love u love u!! Haha Ladies and gentleman u r da best!

[@jarikosonen4079]

Integration by parts and can you make this with Feynman's method also?

[@mahooi]

Thank you!!

[@jeremyhuang7160]

can we use the DI method to solve the integral of sin^2(x) or still have to use the trigonometry method?

[@carultch]

You will end up in an infinite loop if you try to apply it to sin^2(x) or cos^2(x).

[@HYEOL]

I remember I had to do this one in an exam

[@user-kf7is4cl7h]

كم اتمنى ان تكون هذا الدرس مترجم

[@shayandaneshvar]

Hey , can you integrate this function? F(x)=x*tan(x)

[@magnuskonig9136]

This is visual asmr

[@vanityngreed]

beautiful

[@blackpenredpen]

thanks!!!

[@katlover1167]

@vanityngreed Him, the mathematics, or both?

[@spooky066]

i see that supreme and that icy watch okayy professor

[@aponbiswas4508]

thank u,,from Bangladesh

[@venzerbcollections69]

Sir, really fast question, can it be done if u=1+2x, then express the integrand in terms of u, then integrate by parts after?

[@vano__]

hello after 3 month, yes if you don't know yet lol

[@josephshaff5194]

crowd goes wild!

[@uttambhadauriya5635]

put 2x=t then you end up with [te^t/4(1+t)^2].... now we have e^t[(1/(1+t) - 1/(1+t)^2]/4... This takes the form of integral e^x[f(x)+f '(x)] = e^x[f(x)]...hence the answer [e^2x/(1+2x)]/4

[@ravipatani3242]

Can D I method used in xln(x)

[@toto9097]

U didn't multiply integrated part by negative sign when u were taking product of cross elements.

[@awvz_1194]

This problem is in the Stewart Calculus book

[@blackpenredpen]

yea

[@soggy6645]

A lot of the example problems he features are.

[@williamdanilobotelloperez5771]

No necesitamos saber inglés para entender los números increíble explicación