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Question Number 206892 by mathzup last updated on 29/Apr/24

$$find{\int }_0^1\sqrt{1+\sqrt{1+x^2}}dx$$

Answered by Frix last updated on 29/Apr/24

$$t=x+\sqrt{x^2+1}$$$$\Rightarrow$$$$\frac{\sqrt{2}}{4}\int (t^{\frac{1}{2}}+t^{-\frac{1}{2}}+t^{-\frac{3}{2}}+t^{-\frac{5}{2}})dt$$$$\mathrm{Which}\mathrm{is}\mathrm{easy}$$

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