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

The integral of 1/(xsqrt(2x^2-1)) is arctan(sqrt(2x^2-1))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

arctan (2 x^{2} - 1) + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u ^{2} + 1} d u = arctan (u)

= arctan (u)

Substitute back

u = 2 x^{2} - 1

= arctan (2 x^{2} - 1)

Add a constant to the solution

= arctan (2 x^{2} - 1) + C

\int (e^{4 x} - x^{- 1}) d x

\int x arctan (x) ln (1 + x^{2}) d x

\int \frac{1}{x ^{2} + 8 x + 7} d x

\int s^{2} d s

\int \frac{2 x}{5 x + 1} d x

What is the integral of 1/(xsqrt(2x^2-1)) ?
The integral of 1/(xsqrt(2x^2-1)) is arctan(sqrt(2x^2-1))+C