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

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Answer 1 · 2016-08-09T15:25:37

$e^(sin x) + C$

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

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

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