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Chain Rule & Integration by Substitution

Review question

How could we integrate $\tan^3 \theta$?
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Ref: R8694

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Question

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 \[\begin{equation*} \int \frac{\sqrt{x+1}}{x-3} \:dx. \end{equation*}\]