Do the following integrals for fun!

a. For \(C\) the boundary of the square \(|x| \leq 2,|y| \leq 2\),

\[\oint_{C} \frac{d z}{z(z-1)(z-3)^{2}}\]

b.

\[\int_{0}^{\pi} \frac{\sin ^{2} \theta}{13-12 \cos \theta} d \theta\]

c.

\[\int_{-\infty}^{\infty} \frac{d x}{x^{2}+5 x+6}\]

d.

\[\int_{0}^{\infty} \frac{\cos \pi x}{1-9 x^{2}} d x\]

e.

\[\int_{-\infty}^{\infty} \frac{d x}{\left(x^{2}+9\right)(1-x)^{2}}\]

f.

\[\int_{0}^{\infty} \frac{\sqrt{x}}{(1+x)^{2}} d x\]

g.

\[\int_{0}^{\infty} \frac{\sqrt{x}}{(1+x)^{2}} d x\]