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

The integral of (4ln(x))/(x^4) is 4(-(ln(x))/(3x^3)-1/(9x^3))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

4 (- \frac{ln ( x )}{3 x ^{3}} - \frac{1}{9 x ^{3}}) + C

Solution steps

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

Take the constant out:

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

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

Apply Integration By Parts

: - \frac{ln ( x )}{3 x ^{3}} - \int - \frac{1}{3 x ^{4}} d x

= 4 (- \frac{ln ( x )}{3 x ^{3}} - \int - \frac{1}{3 x ^{4}} d x)

\int - \frac{1}{3 x ^{4}} d x = \frac{1}{9 x ^{3}}

= 4 (- \frac{ln ( x )}{3 x ^{3}} - \frac{1}{9 x ^{3}})

Add a constant to the solution

= 4 (- \frac{ln ( x )}{3 x ^{3}} - \frac{1}{9 x ^{3}}) + C

\int (2 e^{x} + 3 sin (x))^{2} d x

\int \frac{1000}{1 + 3 x} d x

\int 3 - 5 x d x

\int 3 sin (2 x) sin (x) d x

What is the integral of (4ln(x))/(x^4) ?
The integral of (4ln(x))/(x^4) is 4(-(ln(x))/(3x^3)-1/(9x^3))+C