Integration by parts: Âº___cos(x)dx | AP Calculus BC | Khan Academy

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Worked example of finding an indefinite integral by applying integration by parts twice, and then obtaining an equation for the desired indefinite integral. Created by Sal Khan.

AP Calculus BC on Khan Academy: Learn AP Calculus BC - everything from AP Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP Test

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never forget the freaken C. EVERY TIME -_-

amyfromandi

you sir are the reason that I still have faith in humanity. You saved my high school grades. Thanks!

jeflaenen

Now that's what I call... MATHEMAGICAL!!

iheartkiecats

You just gotta love integration and calculus!!!Superb video!!!

JohnMmbaga_

At 3:30, looking at this from the end of the video it's hard to tell you changed that subtraction to an addition. I thought it was a subtraction and I didn't get it at all. Thanks for the video, once again my class never covered how to do this problem when you run into what appears to be an infinite loop of integration by parts.

MisterBinx

I know this video is 7 years old but you literally helped me understand integration by parts! Thank U!

JesusMartinez-zuxl

This is great. Thankyou. I do find it amusing that every time he says 'minus' it has to be said twice though.

scottonus

FINALLY!! i've been tryna find out what to do when u get the same integral on both sides for like 2 weeks LOL

willaguirre

Did you just do the whole explanation again just because people might get confused by you substituting a for the original integral? Man, Sal you're such a good person, just unbelievable...

mrnosy

Sal is an absolute freaking saviour oh my gosh we love you man :) like if you agree :D

blendomania

"we got this business right here" :D

awesome video man helped a lot

MefeiesT

I was trying to find something trigonometric to multiply and divide by, because when I imagined the F(x)F(g)=F(x)f(g)+f(x)F(g) solution - I stack, but it's actually that simple. A little wonder.

kingfiend

amazing. thank you sir. God bless you.

dancequeen

How would you solve the integral 5xe^(-2x^2)dx? You're you life saver, Sal!!

bustos

(after trying to solve this on my own for half an hour before watching the vid)
0:31 * *my mind* * : And actually you can solve this problem NEITHER way 😂😂.

yash

wish i could give my tuition fees to you

EA-dlsg

why does the e^x become negative in the second integral

alessandrotassandin

i don't understand why you didn't just take into consideration using L.I.A.T.E, and chosing sinx to be f(x)

piecemage

Why did you just do the same problem twice? I thought your original explanation was perfect

mrnosy

Can someone please explain the equation he writes at 3:30 and then proceeds to enter a slightly different equation at ~4:57. My specific question is why is the integral not added how he wrote it in the original equation?

NauticalAdventure

Integration by parts: Âº___cos(x)dx | AP Calculus BC | Khan Academy

Integration by parts: Âº___cos(x)dx | AP Calculus BC | Khan Academy

Integration by parts: Âºx_cos(x)dx | AP Calculus BC | Khan Academy

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