I tried to solve the following integral using Maple as well as by hand but unable to do so. Can anybody help me in solving the following integral?
$$ \int_{0}^{R} D\pi r^2 (D\pi r^2-1)^B 2\pi \lambda \alpha r e^{-\pi r^2(\alpha \lambda - D ln(Y))} dr $$
In the above equation, $D$, $B$, $Y$, $\alpha$, $\lambda$ are constants
First, it becomes nicer if the constants are simplified. Then the change of variable $x=r^2$ leads to an integral involving the Incomplete Gamma function :
http://mathworld.wolfram.com/IncompleteBetaFunction.html http://www.wolframalpha.com/input/?i=integrate+%28cx-1%29%5EBexp%28-bx%29xdx
The formula given by WolframAlpha can be obtained ourself with a change of variable $X=cx$ and separation into two integrals. Hint : $(X-1)^BX=(X-1)^{B+1}+(X-1)^B$