# How to integrate ∫ (x^2−9)^(3/2) dx?

## $\int {\left({x}^{2} - 9\right)}^{\frac{3}{2}} \mathrm{dx}$ I have used substitution x=3 sec u and can go up to 81 ∫ （sec u)^5 -2 （sec u)^3 +sec u) du. I then try to use t=tan(u/2) to solve ∫ （sec u)^5 du but end up in a mess. Please help.

${x}^{3} / 4 \sqrt{{x}^{2} - 9} - \frac{45}{8} x \sqrt{{x}^{2} - 9} + \frac{243}{8} \ln \left(x + \sqrt{{x}^{2} - 9}\right)$