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Chain Rule & Integration by Substitution

Review question

Can we use integration by substitution on these integrals?
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Ref: R8890

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Question

By using the substitution \(u = 1 - x^2\), or otherwise, evaluate \[\begin{equation*} \int_0^{\frac{1}{2}} \frac{x}{(1-x^2)^2} \:dx. \end{equation*}\]
Evaluate \[\begin{equation*} \int_0^{\pi/6} \frac{\sin \theta \:d\theta}{\cos^3 \theta}. \end{equation*}\]