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

The integral of f(cos(x)) is fsin(x)+C

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integral of f(cos(x))

\int f (cos (x)) d x

f sin (x) + C

Solution steps

\int f cos (x) d x

Take the constant out:

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

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

Use the common integral:

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

= f sin (x)

Add a constant to the solution

= f sin (x) + C

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