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

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

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

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

Solution steps

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

Apply u-substitution

: \int \frac{1}{2 u} d u

= \int \frac{1}{2 u} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} ln ∣ u ∣

Substitute back

u = x^{2} + 2

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

Add a constant to the solution

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

\int \frac{8 x ^{3}}{4 + 2 x ^{4}} d x

15 x

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

5 x^{2} 25 - x^{2}

\int_{0}^{5} (5 + 3 x)^{- 1} d x

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