Prove that: (i) \( \int 1 / \sqrt{\left(1-x^{2}\right)} \cdot d x=\sin ^{-1} x+C \) (ii) \( \int...

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Prove that:
(i) \( \int 1 / \sqrt{\left(1-x^{2}\right)} \cdot d x=\sin ^{-1} x+C \)
(ii) \( \int 1 /\left(1+x^{2}\right) \cdot d x=\tan ^{-1} x+C \)
(iii) \( \int 1 /|x| \sqrt{\left(x^{2}-1\right)} \cdot d x=\sec ^{-1} x+C \)
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