What is the integral of sin(x)sin(2cos(x)) ?

The integral of sin(x)sin(2cos(x)) is 1/2 cos(2cos(x))+C

integral of sin(x)sin(2cos(x))

\int sin (x) sin (2 cos (x)) d x

\frac{1}{2} cos (2 cos (x)) + C

Solution steps

\int sin (x) sin (2 cos (x)) d x

Apply u-substitution

= \int - \frac{sin ( 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 sin (u) d u

Use the common integral:

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

= - \frac{1}{2} (- cos (u))

Substitute back

u = 2 cos (x)

= - \frac{1}{2} (- cos (2 cos (x)))

Simplify

= \frac{1}{2} cos (2 cos (x))

Add a constant to the solution

= \frac{1}{2} cos (2 cos (x)) + C

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