What is the integral of 6cos(x)cos(sin(x)) ?

The integral of 6cos(x)cos(sin(x)) is 6sin(sin(x))+C

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integral of 6cos(x)cos(sin(x))

\int 6 cos (x) cos (sin (x)) d x

6 sin (sin (x)) + C

Solution steps

\int 6 cos (x) cos (sin (x)) d x

Take the constant out:

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

= 6 \cdot \int cos (x) cos (sin (x)) d x

Apply u-substitution

: \int cos (u) d u

= 6 \cdot \int cos (u) d u

Use the common integral:

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

= 6 sin (u)

Substitute back

u = sin (x)

= 6 sin (sin (x))

Add a constant to the solution

= 6 sin (sin (x)) + C

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What is the integral of 6cos(x)cos(sin(x)) ?
The integral of 6cos(x)cos(sin(x)) is 6sin(sin(x))+C