What is the integral of (sin(3ln(x)))/x ?

The integral of (sin(3ln(x)))/x is -1/3 cos(3ln(x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (sin(3ln(x)))/x

\int \frac{sin ( 3 ln ( x ) )}{x} d x

- \frac{1}{3} cos (3 ln (x)) + C

Solution steps

\int \frac{sin ( 3 ln ( x ) )}{x} d x

Apply u-substitution

: \int \frac{sin ( u )}{3} d u

= \int \frac{sin ( u )}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{3} (- cos (u))

Substitute back

u = 3 ln (x)

= \frac{1}{3} (- cos (3 ln (x)))

Simplify

= - \frac{1}{3} cos (3 ln (x))

Add a constant to the solution

= - \frac{1}{3} cos (3 ln (x)) + C

\int \frac{x}{x ^{2} - 7} d x

\int \frac{3 x ^{2}}{( 8 - 3 x ^{3} ) ^{5}} d x

\int - cos (x) x d x

\int \frac{8}{x ln ( 9 x )} d x

\int \frac{1}{a x - b x ^{2}} d x

What is the integral of (sin(3ln(x)))/x ?
The integral of (sin(3ln(x)))/x is -1/3 cos(3ln(x))+C