Question

How do you find the antiderivative of `e^(sinx)*cosx`?

Answer 1

`e^(sin x) + C`

Explanation:

there's a very common pattern there

note generally that `d/dx (e^(f(x))) = f'(x) e^(f(x))`

So `int f'(x) e^(f(x)) dx = int d/dx( e^(f(x))) dx = e^(f(x))+ C`

Here you have

`int d/dx e^(sin x) \ dx = e^(sin x) + C`