Hi

i few question i am having trouble finding the correct answer:

1)$\displaystyle \int_0^\frac{\pi}{2}5x+sin2x dx$

i got $\displaystyle \frac{5\pi^2}{8}+\frac{1}{2}$ however the answers says its $\displaystyle \frac{5\pi^2}{8}+1$

2)$\displaystyle \int_1^4(2+\frac{1}{x})^2 dx$

$\displaystyle \frac{(2+\frac{1}{x})^3}{3}$

$\displaystyle \frac{(2+\frac{1}{4})^3}{3}-\frac{(2+\frac{1}{1})^3}{3}$

which gives me $\displaystyle \frac{33}{4}$ and this is incorrect.

3)$\displaystyle \int_0^1x^2(1-x) dx$

someone tell me how would i start this off.

P.S