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As a minor step in a quantum mechanics problem I need to integrate x * sin(pi*x/a) * sin (2pi*x/a) over the interval 0 to a.

I have had no luck and can't find it in my tables. Do I have to convert it to exponentials and integrate all those terms?

I tried using sin 2y = 2siny cosy to get

[inte] y * 2sin

but that didn't get me anywhere. Help would be greatly appreciated.

I have had no luck and can't find it in my tables. Do I have to convert it to exponentials and integrate all those terms?

I tried using sin 2y = 2siny cosy to get

[inte] y * 2sin

^{2}(y) cos(y) dybut that didn't get me anywhere. Help would be greatly appreciated.

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