Let I = . Proceed as follows:
u = sin x |
dv = ex dx |
du = cos x dx |
v = ex |
Thus

Now use integration by parts on the remaining integral . Use the following assignments:
u = cos x |
dv = ex dx |
du = –sin x dx |
v = ex |
Thus

Note that appears on both sides of this equation. Replace it with I and then solve.

We finally obtain

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