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Fourier Serries - Integration Help

Ok, just attempted another Fourier serries for the half range sine extension of x(l-x) over the range 0<x<l. I havent finished the question yet but before i go any futher i would like to get someone else to have a look over my working if anyone has the time.

The problem and my solution to finding the coeficient bn, are attached and was hopeing someone could take a look at my integration and make sure i didn't make a mistake somewhere. Also, is there a simple way to test to see if i have the right expression for bn?

Thanks

Elbarto