# How do you integrate int e^(sinpix)cospix from [0,pi/2]?

$\frac{1}{\pi} \left({e}^{\sin \left({\pi}^{2} / 2\right)} - 1\right)$
$\frac{d}{\mathrm{dx}} {e}^{\sin \left(\pi x\right)} = \pi \cos \left(\pi x\right) {e}^{\sin \left(\pi x\right)}$ we have
$\int \cos \left(\pi x\right) {e}^{\sin \left(\pi x\right)} \mathrm{dx} = \frac{1}{\pi} \left({e}^{\sin \left({\pi}^{2} / 2\right)} - 1\right)$