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

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

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integral of cos(x)*e^{sin(x)}

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

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

Solution steps

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

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 (x)

= e^{s i n (x)}

Add a constant to the solution

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

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