Integrate Using Trig Substitution integral of ( square root of x^2-9)/(x^3) with respect to x

Solution

trigonometric substitution

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

\frac{1}{6} (arcsec (\frac{1}{3} x) - \frac{1}{2} sin (2 arcsec (\frac{1}{3} x))) + C

Solution steps

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

Apply Trigonometric Substitution:

\frac{1}{6} (arcsec (\frac{1}{3} x) - \frac{1}{2} sin (2 arcsec (\frac{1}{3} x))) + C

= \frac{1}{6} (arcsec (\frac{1}{3} x) - \frac{1}{2} sin (2 arcsec (\frac{1}{3} x))) + C

x \to 1 - lim (\frac{( x - 1 )}{( x ^{2} - 4 )})

(- 3, 3), (5, 9)

x \to - \infty lim (\frac{( x ^{4} - 1 )}{( x ^{3} - 1 )})

\int \frac{( ln ( x ) )}{x} d x

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