What is the integral of x/(5x^2+2) ?

The integral of x/(5x^2+2) is 1/10 ln|5x^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/(5x^2+2)

\int \frac{x}{5 x ^{2} + 2} d x

\frac{1}{10} ln 5 x^{2} + 2 + C

Solution steps

\int \frac{x}{5 x ^{2} + 2} d x

Apply u-substitution

: \int \frac{1}{10 u} d u

= \int \frac{1}{10 u} d u

Take the constant out:

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

= \frac{1}{10} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{10} ln ∣ u ∣

Substitute back

u = 5 x^{2} + 2

= \frac{1}{10} ln 5 x^{2} + 2

Add a constant to the solution

= \frac{1}{10} ln 5 x^{2} + 2 + C

\int 5 5 - 2 x d x

\int x (5 x^{2} + 8)^{10} d x

\int \frac{12 x ^{3} + 8 x ^{2} - 6}{x ^{2}} d x

\int 2 x^{3} - 5 x + 7 d x

\int (4 x^{3} + 3 sin (x) + sec (x) tan (x)) d x

What is the integral of x/(5x^2+2) ?
The integral of x/(5x^2+2) is 1/10 ln|5x^2+2|+C