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

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

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integral of sin(θ)e^{cos(θ)}

\int sin (θ) e^{c o s (θ)} d θ

- e^{c o s (θ)} + C

Solution steps

\int sin (θ) e^{c o s (θ)} d θ

Apply u-substitution

: \int - e^{u} d u

= \int - e^{u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int e^{u} d u

Use the common integral:

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

= - e^{u}

Substitute back

u = cos (θ)

= - e^{c o s (θ)}

Add a constant to the solution

= - e^{c o s (θ)} + C

\int_{1}^{3} x d x

\int e^{2 x} cos (4 x) d x

\frac{d}{d x} ((ln (x))^{- 2})

\int 2 x^{\frac{1}{3}} d x

x \to \infty lim (cos (x))

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