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

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

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

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

Solution steps

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

Apply u-substitution

= \int u^{2} d u

Apply the Power Rule

= \frac{u ^{3}}{3}

Substitute back

u = ln (x) + 1

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

Add a constant to the solution

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

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