Stuck on this definite integral problem I'm stuck on this definite integral problem. I need some constructive hint to proceed further. 
$$\int_0^a (a^2 + x^2)^\frac{5}{2} dx$$
Substituting
$$x = a \cot\theta,$$
I have converted this integral to $$\int_0^a (a \csc\theta)^5 dx.$$
Now I'm unable to proceed further. Kindly help

Hint:
Substitute $x=a\sinh(t)$.
$$a^6\int\cosh^6(t)\,dt=\frac{a^6}{32}\int(\cosh(6t)+6\cosh(4t)+15\cosh(2t)+40)\,dt.$$
