What is the integral of (sqrt(x^2-6))/(x^3) ?

The integral of (sqrt(x^2-6))/(x^3) is -(sqrt(x^2-6))/(2x^2)+1/(2sqrt(6))arcsec(1/(sqrt(6))x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (sqrt(x^2-6))/(x^3)

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

- \frac{x ^{2} - 6}{2 x ^{2}} + \frac{1}{2 6} arcsec (\frac{1}{6} x) + C

Solution steps

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

Apply Integration By Parts

: - \frac{x ^{2} - 6}{2 x ^{2}} - \int - \frac{1}{2 x x ^{2} - 6} d x

= - \frac{x ^{2} - 6}{2 x ^{2}} - \int - \frac{1}{2 x x ^{2} - 6} d x

\int - \frac{1}{2 x x ^{2} - 6} d x = - \frac{1}{2 6} arcsec (\frac{1}{6} x)

= - \frac{x ^{2} - 6}{2 x ^{2}} - (- \frac{1}{2 6} arcsec (\frac{1}{6} x))

Simplify

= - \frac{x ^{2} - 6}{2 x ^{2}} + \frac{1}{2 6} arcsec (\frac{1}{6} x)

Add a constant to the solution

= - \frac{x ^{2} - 6}{2 x ^{2}} + \frac{1}{2 6} arcsec (\frac{1}{6} x) + C

\int \frac{4}{( 3 - x ) ^{2}} d x

\int \frac{e ^{x}}{e + e ^{x}} d x

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

\int arccot (g) x d x

\int \frac{7}{x ^{2} + x - 12} d x

What is the integral of (sqrt(x^2-6))/(x^3) ?
The integral of (sqrt(x^2-6))/(x^3) is -(sqrt(x^2-6))/(2x^2)+1/(2sqrt(6))arcsec(1/(sqrt(6))x)+C