What is the integral of x/(1-2x^2) ?

The integral of x/(1-2x^2) is -1/4 ln|1-2x^2|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of x/(1-2x^2)

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

- \frac{1}{4} ln 1 - 2 x^{2} + C

Solution steps

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

Apply u-substitution

= \int - \frac{1}{4 u} d u

Take the constant out:

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

= - \frac{1}{4} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - \frac{1}{4} ln ∣ u ∣

Substitute back

u = 1 - 2 x^{2}

= - \frac{1}{4} ln 1 - 2 x^{2}

Add a constant to the solution

= - \frac{1}{4} ln 1 - 2 x^{2} + C

What is the integral of x/(1-2x^2) ?
The integral of x/(1-2x^2) is -1/4 ln|1-2x^2|+C