What is the integral of (ln(x^2))/(x^4) ?

The integral of (ln(x^2))/(x^4) is -(2ln(x))/(3x^3)-2/(9x^3)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (ln(x^2))/(x^4)

\int \frac{ln ( x ^{2} )}{x ^{4}} d x

- \frac{2 ln ( x )}{3 x ^{3}} - \frac{2}{9 x ^{3}} + C

Solution steps

\int \frac{ln ( x ^{2} )}{x ^{4}} d x

Apply Integration By Parts

= - \frac{ln ( x ^{2} )}{3 x ^{3}} - \int - \frac{2}{3 x ^{4}} d x

\int - \frac{2}{3 x ^{4}} d x = \frac{2}{9 x ^{3}}

= - \frac{ln ( x ^{2} )}{3 x ^{3}} - \frac{2}{9 x ^{3}}

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= - \frac{2 ln ( x )}{3 x ^{3}} - \frac{2}{9 x ^{3}}

Add a constant to the solution

= - \frac{2 ln ( x )}{3 x ^{3}} - \frac{2}{9 x ^{3}} + C

What is the integral of (ln(x^2))/(x^4) ?
The integral of (ln(x^2))/(x^4) is -(2ln(x))/(3x^3)-2/(9x^3)+C