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Math Help - reduction formula

  1. #1
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    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!
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  2. #2
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    Quote Originally Posted by jackm7 View Post
    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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