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

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

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

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

sin (sin (x)) + C

Solution steps

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

Apply u-substitution

: \int cos (u) d u

= \int cos (u) d u

Use the common integral:

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

= sin (u)

Substitute back

u = sin (x)

= sin (sin (x))

Add a constant to the solution

= sin (sin (x)) + C

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