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Question Number 196688 by cortano12 last updated on 29/Aug/23

Answered by Frix last updated on 29/Aug/23

$$\int \sqrt{x-\sqrt{x^2-4}}dx\stackrel{t=\sqrt{x-\sqrt{x^2-4}}}{=}$$$$=\int \frac{t^4-4}{t^2}dt=\frac{t^3}{3}+\frac{4}{t}=$$$$...$$$$=\frac{2(2x+\sqrt{x^2-4})\sqrt{x-\sqrt{x^2-4}}}{3}+C$$

Commented by cortano12 last updated on 30/Aug/23

$${\mathrm{Euler}}^{\prime }\mathrm{s}\mathrm{Subtitution}$$

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