$ x(t) = \left \{ A(t-\frac{T}{4})(t+\frac{T}{4}) , -T/4<t<T/4\right. $
I tried using the derivative rule to get the fourier series from the square wave, but the answer does not match up to the answer after simply finding the fourier coefficients using the brute force integration method.
$a_k = \frac{AT^2(\pi k cos(\pi k /2) - 2 sin(\pi k /2))}{2 \pi ^3 k ^3} \\ b_k=0 $
Can anyone explain why that is??