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## Homework Statement

I need to find the Fourier series for [itex]f(x)=|x|^3[/itex].

## Homework Equations

[itex]f(x)=|x|^3[/itex]

[itex]A_n=\frac{2}{L}\int_{0}^{L}|x|^3cos{\frac{n\pi x}{L}}dx[/itex]

[itex]\int_{0}^{L}x|x|sin{\frac{n\pi x}{L}}dx[/itex]

## The Attempt at a Solution

Since it is an even function I know that it will be a cosine series and so I set out to find the A coefficient like so:

[itex]A_n=\frac{2}{L}\int_{0}^{L}|x|^3cos{\frac{n\pi x}{L}}dx[/itex]

Through integration by parts I end up with a sine term that goes to zero and some coefficients out in front of an integral that looks like:

[itex]\int_{0}^{L}x|x|sin{\frac{n\pi x}{L}}dx[/itex]

I would really appreciate any help with this particular integral or if someone could point me in the direction of a solution where a Fourier series is calculated for a function with an absolute value to the power>2. Thanks in advance.