Compute the following integrals:

a. \(\int x e^{2 x^{2}} d x\).

b. \(\int_{0}^{3} \frac{5 x}{\sqrt{x^{2}+16}} d x\).

c. \(\int x^{3} \sin 3 x d x\). (Do this using integration by parts, the Tabular Method, and differentiation under the integral sign.)

d. \(\int \cos ^{4} 3 x d x\).

e. \(\int_{0}^{\pi / 4} \sec ^{3} x d x\).

f. \(\int e^{x} \sinh x d x\).

g. \(\int \sqrt{9-x^{2}} d x\)

h. \(\int \frac{d x}{\left(4-x^{2}\right)^{2}}\), using the substitution \(x=2 \tanh u\).

i. \(\int_{0}^{4} \frac{d x}{\sqrt{9+x^{2}}}\), using a hyperbolic function substitution.

j. \(\int \frac{d x}{1-x^{2}}\), using the substitution \(x=\tanh u\).

k. \(\int \frac{d x}{\left(x^{2}+4\right)^{3 / 2}}\), using the substitutions \(x=2 \tan \theta\) and \(x=2 \sinh u\). 1. \(\int \frac{d x}{\sqrt{3 x^{2}-6 x+4}}\).