Techniques of Integration - Integration by Substitution
Techniques of Integration - Integration by Substitution
- Use the substitution \(u^2 = 1 + x\) to find \(\int \frac{x}{2(1+x)\sqrt{1+x}} \mathrm{d}x\).
- Hence find \(\int \tan^{-1} \sqrt{x+1} \mathrm{d}x\)
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Answer:(i) \(\sqrt{1+x} - 2\tan^{-1}\sqrt{1+x} + C\) (ii) \((x+2)\tan^{-1}\sqrt{x+1} - \sqrt{x+1} + C\)
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