What is the integral of (sqrt(36x^2-25))/(x^3) ?

The integral of (sqrt(36x^2-25))/(x^3) is -(sqrt(36x^2-25))/(2x^2)+18/5 arcsec(6/5 x)+C

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integral of (sqrt(36x^2-25))/(x^3)

\int \frac{36 x ^{2} - 25}{x ^{3}} d x

- \frac{36 x ^{2} - 25}{2 x ^{2}} + \frac{18}{5} arcsec (\frac{6}{5} x) + C

Solution steps

\int \frac{36 x ^{2} - 25}{x ^{3}} d x

Apply Integration By Parts

: - \frac{36 x ^{2} - 25}{2 x ^{2}} - \int - \frac{18}{x 36 x ^{2} - 25} d x

= - \frac{36 x ^{2} - 25}{2 x ^{2}} - \int - \frac{18}{x 36 x ^{2} - 25} d x

\int - \frac{18}{x 36 x ^{2} - 25} d x = - \frac{18}{5} arcsec (\frac{6}{5} x)

= - \frac{36 x ^{2} - 25}{2 x ^{2}} - (- \frac{18}{5} arcsec (\frac{6}{5} x))

Simplify

= - \frac{36 x ^{2} - 25}{2 x ^{2}} + \frac{18}{5} arcsec (\frac{6}{5} x)

Add a constant to the solution

= - \frac{36 x ^{2} - 25}{2 x ^{2}} + \frac{18}{5} arcsec (\frac{6}{5} x) + C

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What is the integral of (sqrt(36x^2-25))/(x^3) ?
The integral of (sqrt(36x^2-25))/(x^3) is -(sqrt(36x^2-25))/(2x^2)+18/5 arcsec(6/5 x)+C