What is the antiderivative of $e^(sinx)*cosx$ ?

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Answer 1 · 2016-03-29T19:31:41

$e^sin(x) +C$

To find

$int e^(sin x)cos x dx$

First use the substitution $u = sin x$
$-> du = cos x dx$

Now put the substitution into our expression to obtain:

$int e^u du$

Evaluating this then reversing the substitution and we get:

$e^u +C = e^sin(x) +C$

What is the antiderivative of e^(sinx)*cosxe^(sinx)*cosx?