- Evaluate
\[\begin{equation*}
\int_0^{\tfrac{1}{4} \pi} \tan^3 \theta \:d\theta,
\end{equation*}\]
giving the answer correct to two significant figures.

- By using the substitution \(x+1 = u^2\), or otherwise, find \[\begin{equation*} \int \frac{\sqrt{x+1}}{x-3} \:dx. \end{equation*}\]