# A level maths integration by parts

okay so i got everything other than when i got 8/5 they got 8/15
but also since when could you integrate like that (the second part of the equation it’s like chain rule for integration? idkkk

https://imgur.com/a/KvsbkTG
Original post by esha06
okay so i got everything other than when i got 8/5 they got 8/15
but also since when could you integrate like that (the second part of the equation it’s like chain rule for integration? idkkk
https://imgur.com/a/KvsbkTG

At the start you lose the thirds part of the 2/3 in the integral
Original post by mqb2766
At the start you lose the thirds part of the 2/3 in the integral

righttt it always takes someone else to point out my stupid mistakes to me 😭😭 i feel like i’m gonna lose so many marks that way

but also what is that type of integration called bc you do that with differentiation in chain rule but not with integration. idk if i’m just being stupid or what
Original post by esha06
righttt it always takes someone else to point out my stupid mistakes to me 😭😭 i feel like i’m gonna lose so many marks that way
but also what is that type of integration called bc you do that with differentiation in chain rule but not with integration. idk if i’m just being stupid or what

You can use the reverse chain rule or more generally substitution to integrate integrands of the form
(ax + b)^y
so divide by a(y+1) and the exponent is increased by 1.
Original post by mqb2766
You can use the reverse chain rule or more generally substitution to integrate integrands of the form
(ax + b)^y
so divide by a(y+1) and the exponent is increased by 1.
so like this https://imgur.com/a/2Ul3Dci

so it was just a coincidence that multiplying 4/3 by 5/2 equalled the 8/15 which was the right number
Original post by esha06
so like this https://imgur.com/a/2Ul3Dci
so it was just a coincidence that multiplying 4/3 by 5/2 equalled the 8/15 which was the right number

sort of. If you have a constant, 4/3 here, multiplying the integrand, you can pull it outside and forget about it until the end, then multiply the result by it. Usually you state the reverse chain rule for an integrand llike
(2x+3)^(3/2)
the integral is
1/2 * 2/5 * (2x+3)^(5/2) = 1/5 * (2x+3)^(5/2)
and its easy to verify that differentiating (chain rule) the answer gives the original integrand.

The reverse chain rule should be in the specification for your exam board, so just have a quick look.