What is the integral of 5e^{cos(x)}sin(x) ?

The integral of 5e^{cos(x)}sin(x) is -5e^{cos(x)}+C

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integral of 5e^{cos(x)}sin(x)

\int 5 e^{c o s (x)} sin (x) d x

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

Solution steps

\int 5 e^{c o s (x)} sin (x) d x

Take the constant out:

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

= 5 \cdot \int e^{c o s (x)} sin (x) d x

Apply u-substitution

: \int - e^{u} d u

= 5 \cdot \int - e^{u} d u

Take the constant out:

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

= 5 (- \int e^{u} d u)

Use the common integral:

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

= 5 (- e^{u})

Substitute back

u = cos (x)

= 5 (- e^{c o s (x)})

Simplify

= - 5 e^{c o s (x)}

Add a constant to the solution

= - 5 e^{c o s (x)} + C

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What is the integral of 5e^{cos(x)}sin(x) ?
The integral of 5e^{cos(x)}sin(x) is -5e^{cos(x)}+C