I want to evaluate this integral :
$I=\int d^{n}q\frac{(q^2)^{a}}{(q^2+D)^b}$
It is a n-dimensional multiple integral in cartesian coordinates where $q=\sqrt{\sum_{1}^{n}q_{i}^2}$ is the Euclidean norm and $D$ is a constant.
Observe that the integrand is spherically symmetric so it can be easily solved in spherical coordinates. So ,
$I=(\int_{0}^{\infty}dqq^{n-1}\frac{(q^2)^a}{(q^2+D)^b})(\frac{2\sqrt{\pi}^n}{\Gamma (n/2)})$
The factor $\frac{2\sqrt{\pi}^n}{\Gamma (n/2)}$ is the area of the n-1 dimensional sphere in n dimensions.
So , How do you calculate the remaining integral $\int_{0}^{\infty}dqq^{n-1}\frac{(q^2)^a}{(q^2+D)^b}$ ??