What is the integral of (sqrt(9x^2-25))/(x^3) ?

The integral of (sqrt(9x^2-25))/(x^3) is -(sqrt(9x^2-25))/(2x^2)+9/10 arcsec(3/5 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(9x^2-25))/(x^3)

\int \frac{9 x ^{2} - 25}{x ^{3}} d x

- \frac{9 x ^{2} - 25}{2 x ^{2}} + \frac{9}{10} arcsec (\frac{3}{5} x) + C

Solution steps

\int \frac{9 x ^{2} - 25}{x ^{3}} d x

Apply Integration By Parts

: - \frac{9 x ^{2} - 25}{2 x ^{2}} - \int - \frac{9}{2 x 9 x ^{2} - 25} d x

= - \frac{9 x ^{2} - 25}{2 x ^{2}} - \int - \frac{9}{2 x 9 x ^{2} - 25} d x

\int - \frac{9}{2 x 9 x ^{2} - 25} d x = - \frac{9}{10} arcsec (\frac{3}{5} x)

= - \frac{9 x ^{2} - 25}{2 x ^{2}} - (- \frac{9}{10} arcsec (\frac{3}{5} x))

Simplify

= - \frac{9 x ^{2} - 25}{2 x ^{2}} + \frac{9}{10} arcsec (\frac{3}{5} x)

Add a constant to the solution

= - \frac{9 x ^{2} - 25}{2 x ^{2}} + \frac{9}{10} arcsec (\frac{3}{5} x) + C

\frac{8 x ^{7}}{5 y ^{4}}

\frac{1}{s \cdot ( s + 1 ) ^{2}}

9^{x}

\int \frac{sin ^{2} ( θ )}{cos ( θ )} d θ

x \to 5 lim (x^{2} + 24)

What is the integral of (sqrt(9x^2-25))/(x^3) ?
The integral of (sqrt(9x^2-25))/(x^3) is -(sqrt(9x^2-25))/(2x^2)+9/10 arcsec(3/5 x)+C