3.35: Area and integration

The diagram shows the curve $y=6x-x^{2}$ for $0\leqslant x\leqslant 5$ and the line $y=x$. Find the area of the shaded region.

Find $\displaystyle\int\left(\dfrac{1}{(2x-6)^{3}}+\mathrm{cos}\,x\right)\,\mathrm{d}x$.

Find $\displaystyle\int\dfrac{(x^{4}+1)^{2}}{2x}\,\mathrm{d}x$.