<s>[INST] Integral $\int \sqrt{x+\sqrt{x^2+2}}dx$ $$\int \sqrt{x+\sqrt{x^2+2}}\ dx$$
I tried various solving methods but I am not coming forward. I unformed the term also to ${x+\sqrt{x^2+2} \over \sqrt{x+\sqrt{x^2+2}}}$  and even multiplied with ${\sqrt{x-\sqrt{x^2+2}} \over \sqrt{x-\sqrt{x^2+2}}}$. 
Trigonometric and hyperbolic substitution didn't help either.
 [/INST] HINT: set $t=\sqrt{x+\sqrt{x^2+2}}$ then we get $x=\frac{t^4-2}{2t^2}$ and we have $$dx=\frac{t^4+2}{t^3}dt$$
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