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

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

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

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

- sin (cos (x)) + C

Solution steps

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

Apply u-substitution

= \int - cos (u) d u

Take the constant out:

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

= - \int cos (u) d u

Use the common integral:

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

= - sin (u)

Substitute back

u = cos (x)

= - sin (cos (x))

Add a constant to the solution

= - sin (cos (x)) + C

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