How to evaluate $ \int_{0}^2 x^{26} (x-1)^{17} (5x-3)dx ~~ ?$ How to evaluate $$ \int_{0}^2 x^{26} (x-1)^{17} (5x-3)dx ~~ ?$$
I have tried to evaluate, $$ I = \int_{0}^2 x^{26} (x-1)^{17} (5x-3)dx = 5\int_{0}^2 x^{27} (x-1)^{17} dx - 3\int_{0}^2 x^{26} (x-1)^{17} dx$$ by parts but I am getting very lengthy expressions for both the integrals . Please help. 

$$\frac{d}{dx} x^{a+1} (x-1)^{b+1} = x^a (x-1)^b \left\{(a+b+2)x - (a+1)\right\}$$
So
\begin{align*}
\int x^{26} (x-1)^{17} \left\{(26+17+2)x - (26+1)\right\} dx
&= \int x^{26} (x-1)^{17} (45x - 27) dx \\
&= 9\int x^{26} (x-1)^{17} (5x - 3) dx \\
&= x^{27} (x-1)^{18}
\end{align*}
Thus $$\int x^{26} (x-1)^{17} (5x - 3) dx = \frac{1}{9} x^{27} (x-1)^{18}$$
