Question

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

Answer 1

`sin(e^x)+c`, where c is a constant

Explanation,

Integration by Substitution,

`inte^x*cos(e^x)dx`

let's assume `e^x=t`

then, `e^x*dx=dt`

`intcos(t)dt`

`sin(t)+c`, where c is a constant

Substituting `t=e^x`, we finally get

`sin(e^x)+c`, where c is a constant