Integrating {(x^2) / sqrt[(x^2) - 9] } dx

[iatnogpitw]

Tricky Integral??

Homework Statement

So the problem is to integrate this:

{(x^2) / sqrt[(x^2) - 9] } dx

I cannot, for the life of me, solve this problem, and I know it's not that hard. I have tried using trig substitutions x = 3 cos(theta) and x = 3 sec(theta) but for some reason, maybe a math error, it doesn't work out. Can someone compute this for me and give steps?

 

[Mark44]

Your trig substitution is set up wrong. Draw a right triangle with x as the hypotenuse and 3 as the base. The altitude will be sqrt(x^2 - 9). The substitution is sec(theta) = x/3. Using this substitution should get you to 27\int sec^3(\theta) d\theta. That one requires integration by parts once or twice, if I recall correctly.