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

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

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

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

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

Solution steps

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

Apply u-substitution

= \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)}

Add a constant to the solution

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

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