Integration - Improper Integrals and Convergence

Evaluate each of the following definite integrals.

1. \(\displaystyle\displaystyle\int_{3}^{6} 3x + \frac{2}{(x-5)^{2}} \mathrm{d}x\)
2. \(\displaystyle\displaystyle\int_{0}^{3} \left( \frac{x^{2} + 3x}{\sqrt{x}} \right) \mathrm{d}x\)
3. \(\displaystyle\displaystyle\int_{-1}^{3} x^{4} (x^{2} + 7x) \mathrm{d}x\)
4. \(\displaystyle\displaystyle\int_{0}^{1} \mathrm{e}^{2x} \mathrm{d}x\)