Evaluate and simplify the following integrals: \text { a) } \int\left(3 x+\frac{4}{x}\right) d x \text { b) } \int\left(4 e^{2 x}+\frac{e^{-2 x}}{2}\right) d x \text { c) } \int \frac{x}{\sqrt{x^{2}-9}}

d x \text { d) } \int_{0}^{9}\left(\frac{5 x-29}{5 x^{2}+38 x+21}\right) d x \text { to } 3 \text { significant figures. } e) Calculate the area under the curve defined by the function: y=\frac{\pi}{2}-\frac{6}{\sqrt{x}} between x = 0 and x = 1