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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

6 x + 4 x^{\frac{4}{5}}

\int θ tan (θ) d θ

\int 4 sin (x) - 2 cos (x) d x

\frac{d}{d x} (\frac{3 x}{x ^{2} + 2})

\frac{d}{d x} (x cos (6 x))

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