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Question Number 129212 by bramlexs22 last updated on 13/Jan/21

$$\mathrm{M}=\int \sqrt{\mathrm{x}+\sqrt{{\mathrm{x}}^2+5}}\mathrm{dx}?$$

Answered by TheSupreme last updated on 13/Jan/21

$$x+\sqrt{x^2+5}=t$$

Answered by MJS_new last updated on 13/Jan/21

$$\int \sqrt{x+\sqrt{x^2+5}}dx=$$$$[t=\sqrt{x+\sqrt{x^2+5}}\to dx=\frac{t^4+5}{t^3}dt]$$$$=\int \frac{t^4+5}{t^2}dt=\frac{t^4-15}{3t}=$$$$=\frac{2(2x-\sqrt{x^2+5})\sqrt{x+\sqrt{x^2+5}}}{3}+C$$

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