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

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

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

\int - sin (x) e^{c o s (x)} d x

e^{c o s (x)} + C

Solution steps

\int - sin (x) e^{c o s (x)} d x

Take the constant out:

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

= - \int sin (x) e^{c o s (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 = cos (x)

= - (- e^{c o s (x)})

Simplify

= e^{c o s (x)}

Add a constant to the solution

= e^{c o s (x)} + C

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