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

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

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integral of cos(x)cos(pisin(x))

\int cos (x) cos (π sin (x)) d x

\frac{1}{π} sin (π sin (x)) + C

Solution steps

\int cos (x) cos (π sin (x)) d x

Apply u-substitution

: \int \frac{cos ( u )}{π} d u

= \int \frac{cos ( u )}{π} d u

Take the constant out:

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

= \frac{1}{π} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{π} sin (u)

Substitute back

u = π sin (x)

= \frac{1}{π} sin (π sin (x))

Add a constant to the solution

= \frac{1}{π} sin (π sin (x)) + C

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