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How do you find the antiderivative of $(e^{sin (t)}) \cdot (cos (t))$ $(e^sin(t)) *(cos(t))$ ?

1 Answer

Sep 11, 2016

$e^{sin (t)} + C$ $e^sin(t)+C$

Explanation:

$\int (e^{sin (t)}) cos (t) d t$ $int(e^sin(t))cos(t)dt$

Let sin(t)=u, cos(t)dt=du

Substitute sin(t) with u, cos(t)dt with du

$\int (e^{u}) d u$ $int(e^u)du$

$e^{u} + C$ $e^u+C$

Substitute u with sin(t)

$e^{sin (t)} + C$ $e^sin(t)+C$

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