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) 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

= \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 = - sin (x)

= - e^{- s i n (x)}

Add a constant to the solution

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

\int \frac{9 x ^{2} - 16 x + 4}{x ^{3} - 3 x ^{2} + 2 x} d x

\int sec (a θ) tan (a θ) d θ

y = 2, y = x^{2} - 2

\frac{\partial}{\partial y} (x^{\frac{1}{2}} y^{\frac{1}{2}})

12 x - x^{3}

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