What is the integral of (3ln(x))/(x^2) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (3ln(x))/(x^2)

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

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

Solution steps

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

Take the constant out:

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

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\int \frac{y ^{2}}{y} d y

\int sin^{3} (x) cos^{14} (x) d x

a \to - 1 lim (a)

x \to 0 + lim (x \cdot ln (x^{4}))

\int \frac{1}{x ^{2} ( x ^{2} - 9 )} d x

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