(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let I_{n}=the integral from 0 to pi/2 of sin^{n}xdx

show that (I_{2n+1})/(I_{2n})=(2n+1)/(2n+2)

2. Relevant equations

integral from 0 to pi/2 of sin^{2n}=(2n-1)pi/4n

3. The attempt at a solution

I can't write down all that I've done because it's just too ridiculous. I've tried lots of forms of just trying to manipulate my equation above, which didn't work. I've tried integration by parts for sin^{2n+1}*sinx but I've ended up with the integral of cos^{2}xsin^{2n}x and I can't find a suitable substitution for that. I've been working on this problem forever and it's killing me. If anyone has any suggestions I would be very appreciative.

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# Integration by parts with trig function insanity

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