# How to find reduction formula for $I_n=\int\frac{(px+q)^n}{\sqrt{ax+b}}dx$

I have to find the reduction formula for the following :

$$\int\frac{(px+q)^n}{\sqrt{ax+b}}dx$$

I took this integral from wikipedia. By using parts this is what I got.

$${2a^{-1}(px+q)^{n}\sqrt{ax+b}-2pna^{-1}\int\{px+q}^{n-1}\sqrt{ax+b}dx$$

$$I_n= \int\frac{(px+q)^n}{\sqrt{ax+b}}dx =\frac{1}{a(n+\frac12)} \int \left( \frac{px+q}{ax+b}\right)^n d\left( (ax+b)^{n+\frac12}\right)$$