Integration by Parts of e^(-2x)sin(3x) - Going in a Loop | Integration | Calculus | Glass of Numbers

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In this video, we use the traditional method of integration by parts to find the antiderivative of a product of exponential and trigonometric function: e^(-2x)sin(3x).

It does not matter whether we use u = e^(-2x) or u = sin(3x), we are still going to get back to the original problem. So it looks like we are going in a loop!

Are we making any progress at all?

See another video in which we go in a loop when integrating Sin(3x)Cos(4x):

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Thank you so much for this example, kept getting stuck on a similar problem after the second vdu. Letting udv=B made this so much easier to look at and solve.

krystianhinz