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Integration: Integration by Parts

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I am trying to integrate e to a variable power times sin or cos using integration by parts, but I seem to be going in circles. How is this problem solved?
The trick for solving e times sin or cos is shown using the example Se^x*sinxdx.

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An integral is solved using integration by parts.

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The trick for solving times sin or cos problems is that after 2 iterations, on the right-hand side of the integration by parts equation you end up with the same integral as on the left-hand side, and you add the right-hand integral back to the left.

The form that makes ...

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