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First time user of this forum.

I have a question regarding an integral i've been stuck on for the past few days. I would really appreciate any eye opener into this problem!

How do I find the Fourier coefficients for f(x)=xcos(x), x [-∏,∏]

So when calculating the coefficient b

_{n}I figure that the equation I'll be working with is (1/∏)∫xcos(x)sin(kx)dx (FROM -∏ to ∏).

I keep getting down to 1/2∏∫xsin((k+1)x)dx (FROM -∏ to ∏) + 1/2∏∫xsin((k-1)x)dx (FROM -∏ to ∏) . I some how always get a 0 for b

_{1}. What am I doing incorrectly??