# How do you find the integral of #(e^x)(cosx) dx#?

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I found:

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I tried Integration by Parts (twice) and a little trick...!

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Alternatively, we can use a nice little technique called complexifying the integral.

We notice that

In terms of complex numbers,

We can do a quite simple u-substitution to evaluate the integral:

We can now use Euler's identity again to expand the top. We also multiply by the conjugate of the bottom to simplify the fraction:

We can now quite easily pick out the real parts:

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