I need to verify the value of the following integral $$ 4n(n-1)\int_0^1 \frac{1}{8t^3}\left[\frac{(2t-t^2)^{n+1}}{(n+1)}-\frac{t^{2n+2}}{n+1}-t^4\{\frac{(2t-t^2)^{n-1}}{n-1}-\frac{t^{2n-2}}{n-1} \} \right] dt.$$ The integrand (factor of $4n(n-1)$) included) is the pdf of certain random variable for $n\geq 3$ and hence I expect it be 1. If somebody can kindly put it into some computer algebra system like MATHEMATICA, I would be most obliged. I do not have access to any CAS software.

PS:-I do not know of any free CAS software. If there is any somebody may please share