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

The integral of (sqrt(25x^2-9))/(x^3) is -(sqrt(25x^2-9))/(2x^2)+25/6 arcsec(5/3 x)+C

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integral of (sqrt(25x^2-9))/(x^3)

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

- \frac{25 x ^{2} - 9}{2 x ^{2}} + \frac{25}{6} arcsec (\frac{5}{3} x) + C

Solution steps

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

Apply Integration By Parts

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

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

\int - \frac{25}{2 x 25 x ^{2} - 9} d x = - \frac{25}{6} arcsec (\frac{5}{3} x)

= - \frac{25 x ^{2} - 9}{2 x ^{2}} - (- \frac{25}{6} arcsec (\frac{5}{3} x))

Simplify

= - \frac{25 x ^{2} - 9}{2 x ^{2}} + \frac{25}{6} arcsec (\frac{5}{3} x)

Add a constant to the solution

= - \frac{25 x ^{2} - 9}{2 x ^{2}} + \frac{25}{6} arcsec (\frac{5}{3} x) + C

z \to 0 lim (\frac{z ^{2}}{z})

\int e^{7 x} cos (6 x) d x

n \to \infty lim (0. 6^{n})

x \to 0 + lim (2 + 3 e^{- \frac{3}{x}})

\frac{1}{x - 1}

What is the integral of (sqrt(25x^2-9))/(x^3) ?
The integral of (sqrt(25x^2-9))/(x^3) is -(sqrt(25x^2-9))/(2x^2)+25/6 arcsec(5/3 x)+C