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- Thread starter JI567
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Simon Bridge

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There's a trick - as you noticed, integration by parts gets you the original integral back again with some extra terms, so round and round you go.

The trick is this: put $$I = \int e^{-x}\sin n\pi x\; dx$$ ... integrate the RHS by parts, twice only.

When you've done that, you should see the original integral appear again, with a bunch of other stuff.

Replace the integral with "I" and solve the resulting equation for I.

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http://www.e-academia.cz/solved-math-problems/integration-by-parts.php

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