Definite Integration Questions with Solutions

Integration by parts

Evaluate $\displaystyle \int_{0}^{\Large \frac{\pi}{4}}{x\sec^2{x}}\,dx$

Evaluate $\displaystyle \int_{0}^{1}{e^{\displaystyle x^2}.x^3}\,dx$

Evaluate $\displaystyle \int_{0}^{\Large \frac{\pi}{2}}{x\sin{x}}\,dx$