What is the integral of sin(x)e^{2cos(x)} ?

The integral of sin(x)e^{2cos(x)} is -1/2 e^{2cos(x)}+C

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integral of sin(x)e^{2cos(x)}

\int sin (x) e^{2 c o s (x)} d x

- \frac{1}{2} e^{2 c o s (x)} + C

Solution steps

\int sin (x) e^{2 c o s (x)} d x

Apply u-substitution

= \int - \frac{e ^{u}}{2} d u

Take the constant out:

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

= - \frac{1}{2} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{2} e^{u}

Substitute back

u = 2 cos (x)

= - \frac{1}{2} e^{2 c o s (x)}

Add a constant to the solution

= - \frac{1}{2} e^{2 c o s (x)} + C

What is the integral of sin(x)e^{2cos(x)} ?
The integral of sin(x)e^{2cos(x)} is -1/2 e^{2cos(x)}+C