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Math Help - Reduction Formula

  1. #1
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    Reduction Formula

    Hey there, I've been struggling with this one for quite a while; so much so that I created an account on here so that I could ask for some help

    I(n) = integral of ((e^sinx)(cosx)(sin^n x))

    I need to show that it comes down to I(n) = e - n I(n-1)

    The integral doesn't have any limits, but I'm pretty sure I need to integrate by parts, but I've tried all the different combinations for u and dv/dx and haven't gotten anywhere.

    Thanks for the help
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  2. #2
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    Re: Reduction Formula

    First make the substitution y= sin(x). What does that integral become? Now use integration by parts.
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  3. #3
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    Re: Reduction Formula

    Quote Originally Posted by HallsofIvy View Post
    First make the substitution y= sin(x). What does that integral become? Now use integration by parts.
    Wow I never even thought of doing a substitution on a reduction formula question. I've been used to doing it by parts.

    Yh that really simplifies things, thanks
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  4. #4
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    Re: Reduction Formula

    Quote Originally Posted by HallsofIvy View Post
    First make the substitution y= sin(x). What does that integral become? Now use integration by parts.
    I get to I(n) = (y^n)(e^y) - n I(n-1)

    In order for me to prove what I need to, I must show that (y^n)(e^y) = e which I'm pretty sure isn't the case. Any tips on what I can do?

    Thanks
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  5. #5
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    Re: Reduction Formula

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