What is the integral of (cos(9x)) ?

The integral of (cos(9x)) is 1/9 sin(9x)+C

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integral of (cos(9x))

\int (cos (9 x)) d x

\frac{1}{9} sin (9 x) + C

Solution steps

\int cos (9 x) d x

Apply u-substitution

: \int cos (u) \frac{1}{9} d u

= \int cos (u) \frac{1}{9} d u

Take the constant out:

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

= \frac{1}{9} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{9} sin (u)

Substitute back

u = 9 x

= \frac{1}{9} sin (9 x)

Add a constant to the solution

= \frac{1}{9} sin (9 x) + C

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