Question

Integrate the following function with respect to $x$:
$e^x\cosh x$

Answer 1

Certainly this is found most easily by converting to exponentials, giving
$e^x\cos hx=\frac{1}{2}{e}^{2x}+\frac{1}{2}$
$\int e^x\cos hxdx=\frac{1}{4}{e}^{2x}+\frac{1}{2}x+constant$