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So my question requires the picture of a graph so here it is. I'm trying to do part $(a)$ and I have worked out all the way up to this part:

$C_k=\frac{1}{2} \int_T \! te^\frac{-j2\pi kt}{T} \, \mathrm{d} t$

And the solutions tab confirms my progress so far. The problem is I have no idea how to continue from here. I understand that you have to integrate by parts from -1 to 1 but....I just don't get how the solutions got the answer that it did. Not even wolfram agrees. How in the world did the solutions go from the integral step to the integrated step?

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First, please make your question self-contained next time, i.e. put the actual problem into the question instead of simply linking to it. As for the integration - the following should help math.stackexchange.com/questions/211089 – fgp Oct 14 '12 at 11:25

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