What is the integral of cos(t)e^{sin(t)} ?

The integral of cos(t)e^{sin(t)} is e^{sin(t)}+C

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integral of cos(t)e^{sin(t)}

\int cos (t) e^{s i n (t)} d t

e^{s i n (t)} + C

Solution steps

\int cos (t) e^{s i n (t)} d t

Apply u-substitution

= \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= e^{u}

Substitute back

u = sin (t)

= e^{s i n (t)}

Add a constant to the solution

= e^{s i n (t)} + C

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What is the integral of cos(t)e^{sin(t)} ?
The integral of cos(t)e^{sin(t)} is e^{sin(t)}+C