How do you find the antiderivative of $(cos 2x)e^(cos 2x)$ ?

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Answer 1 · 2015-03-06T02:28:22

I don't think you can (in finite form).

You can find the antiderivative of $(sin2x)e^cos(2x)$ or of $(cos2x)e^sin(2x)$ by substitution.

The antiderivative of $(sin2x)e^cos(2x)$ is $-1/2e^cos(2x)+C$ .
(Let $u=cos(2x)$ , so $du=-2sin(2x)dx$ )

The antiderivative of $(cos2x)e^sin(2x)$ is $1/2e^sin(2x)+C$ .
(Let $u=sin(2x)$ , so $du=2cos(2x)dx$ )

How do you find the antiderivative of (cos 2x)e^(cos 2x)(cos 2x)e^(cos 2x)?