1. ## reduction formula

hey there, first time poster, long time struggler...so i need some help with a problem.

it says to find the reduction formula for the integral (e^x)(sin x)^n in terms of the integral (e^x)(sin x)^n-2.

i know its integration by parts but i have no idea what to do for my substitutions because (sin x)^n on its own is difficult enough so how do I incorporate the e^x?

cheers!

2. Originally Posted by jackm7
hey there, first time poster, long time struggler...so i need some help with a problem.

it says to find the reduction formula for the integral (e^x)(sin x)^n in terms of the integral (e^x)(sin x)^n-2.

i know its integration by parts but i have no idea what to do for my substitutions because (sin x)^n on its own is difficult enough so how do I incorporate the e^x?

cheers!
Integration by parts twice. For the first use

$u = \sin^n x,\; dv = e^x\,dx$

so

$du = n \sin ^{n-1}x \cos x\, dx \;\;v = e^x$

and

$e^x \sin^n x - n \int e^x \sin ^{n-1}x \cos x\,dx$

For the second by parts

$u = \sin ^{n-1}x \cos x,\; dv = e^x\,dx$

and use some identites - see how that goes.

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# successive reduction sin^n x

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