What is the integral of 4sin(x)e^{cos(x)} ?

The integral of 4sin(x)e^{cos(x)} is -4e^{cos(x)}+C

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integral of 4sin(x)e^{cos(x)}

\int 4 sin (x) e^{c o s (x)} d x

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

Solution steps

\int 4 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

= 4 \cdot \int sin (x) e^{c o s (x)} d x

Apply u-substitution

: \int - e^{u} d u

= 4 \cdot \int - e^{u} d u

Take the constant out:

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

= 4 (- \int e^{u} d u)

Use the common integral:

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

= 4 (- e^{u})

Substitute back

u = cos (x)

= 4 (- e^{c o s (x)})

Simplify

= - 4 e^{c o s (x)}

Add a constant to the solution

= - 4 e^{c o s (x)} + C

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What is the integral of 4sin(x)e^{cos(x)} ?
The integral of 4sin(x)e^{cos(x)} is -4e^{cos(x)}+C