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{3 - x ^{2}}{x ^{3} - x} d x

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

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

\int \frac{7 x + 3}{x ^{2} + 3 x - 4} d x

\int x sin (1 n x) 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