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

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

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

\int e^{2 s i n (x)} cos (x) d x

\frac{1}{2} e^{2 s i n (x)} + C

Solution steps

\int e^{2 s i n (x)} cos (x) d x

Apply u-substitution

: \int \frac{e ^{u}}{2} d u

= \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 sin (x)

= \frac{1}{2} e^{2 s i n (x)}

Add a constant to the solution

= \frac{1}{2} e^{2 s i n (x)} + C

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