What is the integral of (sqrt(x^2-81))/(x^3) ?

The integral of (sqrt(x^2-81))/(x^3) is -(sqrt(x^2-81))/(2x^2)+1/18 arcsec(1/9 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^2-81))/(x^3)

\int \frac{x ^{2} - 81}{x ^{3}} d x

- \frac{x ^{2} - 81}{2 x ^{2}} + \frac{1}{18} arcsec (\frac{1}{9} x) + C

Solution steps

\int \frac{x ^{2} - 81}{x ^{3}} d x

Apply Integration By Parts

: - \frac{x ^{2} - 81}{2 x ^{2}} - \int - \frac{1}{2 x x ^{2} - 81} d x

= - \frac{x ^{2} - 81}{2 x ^{2}} - \int - \frac{1}{2 x x ^{2} - 81} d x

\int - \frac{1}{2 x x ^{2} - 81} d x = - \frac{1}{18} arcsec (\frac{1}{9} x)

= - \frac{x ^{2} - 81}{2 x ^{2}} - (- \frac{1}{18} arcsec (\frac{1}{9} x))

Simplify

= - \frac{x ^{2} - 81}{2 x ^{2}} + \frac{1}{18} arcsec (\frac{1}{9} x)

Add a constant to the solution

= - \frac{x ^{2} - 81}{2 x ^{2}} + \frac{1}{18} arcsec (\frac{1}{9} x) + C

\int + \frac{x}{3 x ^{2} + 1} d x

\frac{d}{d x} ((2 x^{3} + 5)^{10})

\int sec (x) d x

\frac{d}{d x} (\frac{e ^{x}}{x} + ln (x))

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

What is the integral of (sqrt(x^2-81))/(x^3) ?
The integral of (sqrt(x^2-81))/(x^3) is -(sqrt(x^2-81))/(2x^2)+1/18 arcsec(1/9 x)+C