OpenStudy (anonymous):

The integral of 1/(x^2+9)^(3/2)dx Ive been trying to solve this for 2 hours please help!

6 years ago
OpenStudy (abb0t):

\[\int\limits \frac{ 1 }{ \sqrt{(x^2+9)^3} }dx\]

6 years ago
OpenStudy (anonymous):

Thats the problem Im doing...But its to the power of (3/2)

6 years ago
OpenStudy (anonymous):

hey, i couldn't figure out the substitution by inspection so i looked up the step by step on wolfram alpha, it's a tan substitution...

6 years ago
OpenStudy (sirm3d):

rewrite \[\sqrt{(x^2+9)^3}\] as \[\left(\sqrt{x^2+9}\right)^3\] trigonometric substitution \[x=3\tan \theta\] follows

6 years ago
OpenStudy (abb0t):

\[(a)^\frac{ 3 }{ 2 } = \sqrt[2]{a^3}\] @sirm3d has the right idea. Use trig subsitution.

6 years ago