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Question Number 198403 by Mingma last updated on 19/Oct/23

Answered by MM42 last updated on 19/Oct/23

$$\sqrt{x+2}=u\Rightarrow x=u^2-2\Rightarrow dx=2udu$$$$\Rightarrow \int \frac{2udu}{u^2-u-2}=\frac{2}{3}\int (\frac{2}{u-2}+\frac{1}{u+1})du$$$$=\frac{4}{3}ln(u-2)+\frac{2}{3}ln(u+1)+c$$$$=\frac{4}{3}ln(\sqrt{x+2}-2)+\frac{2}{3}ln(\sqrt{x+2}+1)+c✓$$$$$$

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