# How do you use Integration by Substitution to find inte^x*cos(e^x)dx?

Jul 28, 2014

$\sin \left({e}^{x}\right) + c$, where c is a constant

Explanation,

Integration by Substitution,

$\int {e}^{x} \cdot \cos \left({e}^{x}\right) \mathrm{dx}$

let's assume ${e}^{x} = t$

then, ${e}^{x} \cdot \mathrm{dx} = \mathrm{dt}$

$\int \cos \left(t\right) \mathrm{dt}$

$\sin \left(t\right) + c$, where c is a constant

Substituting $t = {e}^{x}$, we finally get

$\sin \left({e}^{x}\right) + c$, where c is a constant