What is the integral of 1/(xsqrt(4x^2-1)) ?

The integral of 1/(xsqrt(4x^2-1)) is arctan(sqrt(4x^2-1))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 1/(xsqrt(4x^2-1))

\int \frac{1}{x 4 x ^{2} - 1} d x

arctan (4 x^{2} - 1) + C

Solution steps

\int \frac{1}{x 4 x ^{2} - 1} d x

Apply u-substitution

= \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 = 4 x^{2} - 1

= arctan (4 x^{2} - 1)

Add a constant to the solution

= arctan (4 x^{2} - 1) + C

What is the integral of 1/(xsqrt(4x^2-1)) ?
The integral of 1/(xsqrt(4x^2-1)) is arctan(sqrt(4x^2-1))+C