# Math Help - Reduction Formula

1. ## 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

2. ## Re: Reduction Formula

First make the substitution y= sin(x). What does that integral become? Now use integration by parts.

3. ## Re: Reduction Formula

Originally Posted by HallsofIvy
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

4. ## Re: Reduction Formula

Originally Posted by HallsofIvy
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

5. ## Re: Reduction Formula

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