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

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

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integral of cos(θ)e^{sin(θ)}

\int cos (θ) e^{s i n (θ)} d θ

e^{s i n (θ)} + C

Solution steps

\int cos (θ) e^{s i n (θ)} d θ

Apply u-substitution

: \int e^{u} d u

= \int e^{u} d u

Use the common integral:

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

= e^{u}

Substitute back

u = sin (θ)

= e^{s i n (θ)}

Add a constant to the solution

= e^{s i n (θ)} + C

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