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

So I have to find the fourier series for [tex]sin^{5}(x)[/tex].

2. Relevant equations

I know the [tex]a_{n}[/tex] in:

[tex]\frac{a_{0}}{2} + \sum^{\infty}_{n=1}a_{n}cos_{n}x + \sum^{\infty}_{n=1}b_{n}sin_{n}x[/tex]

goes to zero, which leaves me with taking the [tex]b_{n}[/tex].

3. The attempt at a solution

So what I got so far is trying to integrate to find [tex]b_{n}[/tex].

[tex]b_{n} = \frac{1}{\pi} \int^{\pi}_{-\pi} sin^{5}(x)sin(nx)[/tex]

But I am not sure how to proceed from here, do I make use of [tex]sin^{2}(x)=1/2(1-cos2x)[/tex] and [tex]cos^{2}(x)=1/2(1+sin2x)[/tex]?

Am I even going in the right direction?

edit:

I just plugged it into Maple and got:

[tex]\frac{1}{\pi}\left( \frac{sin((n-5)x}{32(n-5)} - \frac{sin((n+5)x}{32(n+5)} - \frac{5sin((n-3)x}{32(n-3)} + \frac{5sin((n-1)x}{16(n-1)} - \frac{5sin((n+1)x}{16(n+1)} \right)^{\pi}_{-\pi}[/tex]

is this the direction I need to go in?

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# Homework Help: The Fourier Series of Sin^5(x)

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