Reduction formula for integral of sec^n(x)

[@teavea10]

I watched the video twice. The secant time I finally got it.

[@jadewolf3416]

haha!

[@ozi-g-be]

Ha🤣

[@jasonng04]

Stop it lol

[@krabard]

ba dum tss!

[@nicoliz1]

Man had to watch twice to make this joke

[@ayushi9797]

Best math teaching YT channel. I watch you while having study breaks when I eat so I don't feel guilty wasting time.

[@sayazor]

Valeu!

[@mamadetaslimtorabally7363]

This is so beautiful. That's the elegancy of Mathematics. What a great work. I admire all the workings. Thank you dear.

[@rice_eater-h8z]

Your badass lectures are more addictive than any netflix series...

[@science-y9209]

This channel is really underrated...

[@adandap]

I tried to teach my dog calculus, but she just tilts her head and looks puzzled.

[@etiennevanwyk5700]

I must be a dog 😂

[@illuminoeye_gaming]

thank you goat you saved my worksheet

[@周世恩-b9c]

I'm clearly understand this formula now!!! Thanks!!!

[@canyon_online]

this is awesome bprp thanks for taking my request! #YAY

[@owamimasilela5248]

Thank you so much for helping. I finally understand this.

[@wawaT100]

Thanks man...very helpful..downloaded ur video to watch it over and over.

[@eltonrodrigues2331]

Man, you're awesome. This is awesome!

[@nitayderei]

You are the best man!

[@vatsalpandya7626]

I already knew this formula but just wanted to know his way of solving the problem And I enjoined/nice

[@rajendramisir3530]

Thanks for sharing your way of showing this result. Your explanation is clear and understandable. I enjoy watching your videos.

[@holyshit922]

My proposition for reduction formula is Int(1/(a^2+x^2)^ndx) because it is quite useful after partial fraction decomposition and completing the square quadratic factors

[@aarushjaiswal6600]

Do you have any idea on how to do that? , I have been trying for ages

[@theultimate2345]

@@aarushjaiswal6600 substitute x=a.tan@ then it will reduce to the integral form of cos@^2n-2 , then you can apply reduction formula for it.

[@wristdisabledwriter2893]

“Please do not say zero” lol

[@juullibee]

ahh this was so helpful thank you sm king

[@chloroflamew211]

If you still interested in what we think of this reduction formula I think that I hate doing them but it's nice at the end if it's right, and are cool to see.

[@hritikmitha9514]

Excellent explanation. Thanks!

[@paultoutounji3582]

You are just extraordinary : it's a great pleasure to follow you !

[@pranavsuren9489]

1:01 n=-1 is the easiest cuz it's integral cosdx

[@antonsebastian6484]

n=0 is easier :)

[@playboy6548]

@@antonsebastian6484 he said except 0

[@MitchelLarsen]

Except that it's not. When n=-1 you are looking for the integral of cosine because 1/secx = cosx so the integral of (secx)^n when n=-1 is sinx, not cosx

[@chebukatigodwinmk8523]

wonderful, I have now understood the complexity in such questions

[@danielbolanos6269]

Nice work man, your videos have been really helpful to me. I really appreciate our videos.

[@danielbolanos6269]

your videos.*

[@kepler4192]

Communism

[@NK-ij5dh]

Always great 👍Keep going pro

[@hachemimokrane2810]

je deviens un fan des integrales bravo mr

[@masumbakapalu4980]

its well explained.. u are doing a great job sir

[@rahmehelsaaiedeh7983]

Amazing 😊 thank you i finally got it 🙏🏻💜

[@augustussorci5365]

dude, thank you so much

[@ayandas8299]

Thank you for all your videos!!

[@felixtubb943]

Loved the video my dude

[@Lu_Ca]

can you consider to upload a 1080p video? if not, why? almost any phone can support it

[@blackpenredpen]

I only use webcam to record. : )

[@lalynelombardi623]

Thank you so much!! I needed help and you helped!

[@diewoelfekommen1]

*in tuuuuh grationbyparts* (love your videos, even though I'm far from understanding everything ;) keep it up!)

[@philp4684]

Strictly speaking, I don't think that formula works for n = 2 either, unless you explicitly add the constant of integration.

[@RafaxDRufus]

It actually works

[@chrthebestdamour2544]

it does work, if n = 2, then the formula gives: => integral(sec^(2)x dx) = [sec^(n-2)x tan(x)]/(2-1) + (2 - 2)/(2 -1) * integral(sec^(2-2)x dx) => integral(sec^(2) dx) = (sec^(0)x * tanx)/1 + 0/1 * integral(sec^(2-2)x dx) but sec^(0)x is basically (sec x)^0 wich is equals to 0, and the second terme is also equals to 0 so we end up with just integral(sec^(2)x dx) = tan(x) + C wich is the basic formula :)

[@philp4684]

Chrthebest Damour - But, as I pointed out in my previous reply, the constant of integration is missing from that result, so it's not a complete solution.

[@chrthebestdamour2544]

Oh well yes indeed but then the constant has to be added for all n, but maybe because the formula has still an integral, he didn't add the constant (i added the constant on my previous reply)

[@philp4684]

@@chrthebestdamour2544 - You're correct that the explicit C isn't necessary for n > 2 because the integral on the right hand side implicitly has a C. But the problem is that when n = 2, the C resulting from that integration gets erased because it is multiplied by (n - 2) / (n - 1).

[@ssdd9911]

is there also a reduction formula for integral of sin^n(x)?

[@thecuriouskid4481]

Yes man there is and for cos^n (x) too

[@bmw123ck]

Yees, the reduction formula for sin(x)^n and cos(x)^n is the half-angle formula for sine and cosine. As an example sin(x)^2=1/2-cos(2x)/2 and cos(x)^2=1/2+cos(2x)/2. If the power is odd, you leave one sine or cosine outside the reduction and use them at the end to u-sub

[@TheBlueboyRuhan]

Since the MAT 2018 paper will take place in a few weeks time could you maybe do previous MAT papers; to help those who will take it?

[@mozacrabs4175]

man i love you

[@rosiewest9034]

you are fantastic

[@GreenMeansGOF]

Are we assuming n > 1 or n any integer besides 1?

[@SAKSHAMIITR]

n is a whole number

[@prakashwagh853]

Nice video

[@letsseepaulallenscard.6604]

I recommended this video to my cat

[@quahntasy]

I am here early. Loved the video!

[@dwghtanderson8423]

great man

[@Emre_369]

Where is the C?

[@suryadisuryadi7193]

can you post video about laplace transformation?

[@blackpenredpen]

antonius suryadi check my playlists

[@vriskanon8183]

thats super cool

[@parthasarathimanna8790]

Why you do DI method for 2 times ?

[@cemates1156]

SEN VAR YA ADAMSİN ADAM

[@ahmedatifabrar7698]

Thank you!

[@arnabmusouwir9018]

But but ...... There is still the integral

[@jordanshemilt6065]

You sub in again. Sorta like looping it about till you get to 3.

[@arnabmusouwir9018]

😫 not again

[@jjeherrera]

It's a recursive formula. You may apply it repeatedly until you get to the n you're interested in. If you wish, you may write down a table with the result for each n (Or look it up at a table of integrals if you don't have the time, but that would be cheating, wouldn't it? :-) ) (A symbolic language is an option too. Still cheating :-) ).

[@yxlxfxf]

Yeah that's why it's called a "reduction" formula.

[@arnabmusouwir9018]

I see

[@beverlyfrancis8433]

Sec^n.... Can you tell me why you did not write sec ^n-3 on left, but wrote ^n-2please?

[@MitchelLarsen]

Chain rule

[@THECONNECTORMAN]

@@MitchelLarsen thx,

[@omarmagdi2732]

I love you!

[@Caesarix2001]

gracias!!!!

[@saharhaimyaccov4977]

4:41 why you dony writing that (secX)^(n-2)=secX^n/secX^2 and then (tanX/secX )^2= sinX^2.

[@mfechojerase8023]

I've been trying to crack that like 4 a 1000 yrs

[@arandompersononyoutube3739]

You didn't put + c at the end.

[@farahnsour8109]

thanks alot

[@pedrocasimiro5796]

Why it doesn't work at sec^4

[@nishantshrestha5325]

love it

[@kirillandrianov953]

ненавижу эту формулу, интегральное исчисление и весь курс математического анализа!!!

[@yashkrishnatery9082]

What is (-1)^π Or (-1)^e

[@unknownanonymous5914]

+yash krishnatery -1 can be expressed as its complex definition which is i^2 or (-1 + 0i). Thus, our question is changed into (-1 + 0i)^π, (-1 + 0i)^e or i^2π, i^2e And we then use complex analysis to solve those expressions to get our answer.

[@pavelgorokhov2976]

Both are infinite countable sets of complex numbers on a circle of radius 1.

[@asadyamin4867]

(-1)^pi = (i^2)^pi = i^2pi = (e^(pi/2)i)^2pi = e^(pi^2 * i)= pi^2 radians around a unit circle in the complex plane which is about right or something like that I probably messed up tho

[@Senesoul]

love u

[@motekkz9997]

My teacher gives us to integrate sec^1412 in exam and it was unexpected 😅

[@science-y9209]

Did you solve it?

[@science-y9209]

I mean.. it would be a very lengthy process

[@xxfazenoscoper360doesnosco7]

N0ice

[@crystalwang4304]

great video... calculus is so annoying

[@frielparna2853]

please make Indonesian subtitles

[@beverlyfrancis8433]

But you were exellent though.

[@pdisp]

But it doesn't work for sec^4(X)..

[@SAKSHAMIITR]

It works

[@Riiisuu]

ooo I’ve done this before

[@Thanos7562-x]

ANY INDIAN?

[@MatchaMoji]

I love you

[@motekkz9997]

Sec^1412 !?

[@jordanshemilt6065]

Tbh i learnt this in sixth form but we had to do much worse things.

[@beverlyfrancis8433]

I hate it with a passion!

[@manthansunilhalarnkar]

Was this a formula, strange ha!

[@001agentplatipus]

sorry i don't own any pet😐😐

[@denizhankeles1784]

+++++++++

[@shivammalluri6403]

don't say zero please

[@muneebahmad7729]

Blackpenredpen #YAY

[@Winniex78]

Fun

[@BluePi3142]

I hate this... #jk #yay