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

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

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

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

Solution steps

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

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= \frac{u ^{2}}{2}

Substitute back

u = ln (x) + 2

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

Add a constant to the solution

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

\int x^{3} \cdot arctan (x) d x

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

\int x (5 - 2 x)^{\frac{1}{3}} d x

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

\int \frac{e ^{2 w}}{1 - e ^{2 w}} d w

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