What is the integral of x/(3x^2+6) ?

The integral of x/(3x^2+6) is 1/6 ln|3x^2+6|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of x/(3x^2+6)

\int \frac{x}{3 x ^{2} + 6} d x

\frac{1}{6} ln 3 x^{2} + 6 + C

Solution steps

\int \frac{x}{3 x ^{2} + 6} d x

Apply u-substitution

= \int \frac{1}{6 u} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{6} ln ∣ u ∣

Substitute back

u = 3 x^{2} + 6

= \frac{1}{6} ln 3 x^{2} + 6

Add a constant to the solution

= \frac{1}{6} ln 3 x^{2} + 6 + C

What is the integral of x/(3x^2+6) ?
The integral of x/(3x^2+6) is 1/6 ln|3x^2+6|+C