What is the integral of cos(4x)sin(sin(4x)) ?

The integral of cos(4x)sin(sin(4x)) is -1/4 cos(sin(4x))+C

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integral of cos(4x)sin(sin(4x))

\int cos (4 x) sin (sin (4 x)) d x

- \frac{1}{4} cos (sin (4 x)) + C

Solution steps

\int cos (4 x) sin (sin (4 x)) d x

Apply u-substitution

: \int cos (u) sin (sin (u)) \frac{1}{4} d u

= \int cos (u) sin (sin (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 cos (u) sin (sin (u)) d u

Apply u-substitution

: \int sin (v) d v

= \frac{1}{4} \cdot \int sin (v) d v

Use the common integral:

\int sin (v) d v = - cos (v)

= \frac{1}{4} (- cos (v))

Substitute back

= \frac{1}{4} (- cos (sin (4 x)))

Simplify

= - \frac{1}{4} cos (sin (4 x))

Add a constant to the solution

= - \frac{1}{4} cos (sin (4 x)) + C

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