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

The integral of sin(4x)e^{cos(4x)} is -1/4 e^{cos(4x)}+C

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

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

- \frac{1}{4} e^{c o s (4 x)} + C

Solution steps

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

Apply u-substitution

: \int sin (u) e^{c o s (u)} \frac{1}{4} d u

= \int sin (u) e^{c o s (u)} \frac{1}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int sin (u) e^{c o s (u)} d u

Apply u-substitution

: \int - e^{v} d v

= \frac{1}{4} \cdot \int - e^{v} d v

Take the constant out:

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

= \frac{1}{4} (- \int e^{v} d v)

Use the common integral:

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

= \frac{1}{4} (- e^{v})

Substitute back

= \frac{1}{4} (- e^{c o s (4 x)})

Simplify

= - \frac{1}{4} e^{c o s (4 x)}

Add a constant to the solution

= - \frac{1}{4} e^{c o s (4 x)} + C

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What is the integral of sin(4x)e^{cos(4x)} ?
The integral of sin(4x)e^{cos(4x)} is -1/4 e^{cos(4x)}+C