What is the integral of (ln(6x))/(x^3) ?

The integral of (ln(6x))/(x^3) is -(ln(6x))/(2x^2)-1/(4x^2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (ln(6x))/(x^3)

\int \frac{ln ( 6 x )}{x ^{3}} d x

- \frac{ln ( 6 x )}{2 x ^{2}} - \frac{1}{4 x ^{2}} + C

Solution steps

\int \frac{ln ( 6 x )}{x ^{3}} d x

Apply Integration By Parts

: - \frac{ln ( 6 x )}{2 x ^{2}} - \int - \frac{1}{2 x ^{3}} d x

= - \frac{ln ( 6 x )}{2 x ^{2}} - \int - \frac{1}{2 x ^{3}} d x

\int - \frac{1}{2 x ^{3}} d x = \frac{1}{4 x ^{2}}

= - \frac{ln ( 6 x )}{2 x ^{2}} - \frac{1}{4 x ^{2}}

Add a constant to the solution

= - \frac{ln ( 6 x )}{2 x ^{2}} - \frac{1}{4 x ^{2}} + C

\int 1 + 4 x^{3} (12 x^{2}) d x

\int (2 x - 3)^{6} d x

\int \frac{3}{e ^{x} + 3} d x

\int \frac{8}{1 - x ^{2}} d x

\int \frac{ln ( x ^{\frac{1}{2}} )}{x} d x

What is the integral of (ln(6x))/(x^3) ?
The integral of (ln(6x))/(x^3) is -(ln(6x))/(2x^2)-1/(4x^2)+C