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

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

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integral of (cos(ln(9x)))/x

\int \frac{cos ( ln ( 9 x ) )}{x} d x

sin (ln (9 x)) + C

Solution steps

\int \frac{cos ( ln ( 9 x ) )}{x} d x

Apply u-substitution

: \int \frac{cos ( ln ( u ) )}{u} d u

= \int \frac{cos ( ln ( u ) )}{u} d u

Apply u-substitution

: \int cos (v) d v

= \int cos (v) d v

Use the common integral:

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

= sin (v)

Substitute back

= sin (ln (9 x))

Add a constant to the solution

= sin (ln (9 x)) + C

\int (3 x - 2)^{- 11} d x

n = 1 \sum \infty \frac{2}{n ( n + 3 )}

x \to 5 lim (4 x - 3 x^{2})

x \to 5 lim (x^{2} + 2 x - 35)

y = 3 csc^{2} (5 x)^{3}

What is the integral of (cos(ln(9x)))/x ?
The integral of (cos(ln(9x)))/x is sin(ln(9x))+C