step-by-step solution unavailable (( possible intermediate steps ))

Question

When using the (( WolframAlpha["integrate 1/(2+Sqrt[1-x]+Sqrt[1+x])"])) function to find integration steps, this message appears to me what is the explanation and why?

As an example, for $\int \frac{1}{\sqrt{1-x}+\sqrt{x+1}+2} dx$

$$ \int \frac{1}{2+\sqrt{1-x}+\sqrt{1+x}} \, dx\approx \left(\sqrt{x+1}+\left(-\frac{1}{\sqrt{x+1}+1}-1\right) \sqrt{1-x}+\frac{1}{\sqrt{x+1}+1}-\frac{2 \left(0.707107 \sqrt{x+1}\right)}{\sin }\right)+C $$

I don't get the steps

Why does this happen?

Answer 1

While Mathematica and Wolfram Alpha can't produce the step-by-step for most of the integrals, there is a Rubi package for integration is available:

<< Rubi`
rubiSol = Steps[Int[1/(2 + Sqrt[1 - x] + Sqrt[1 + x]), x]];
mathSol = Integrate[1/(2 + Sqrt[1 - x] + Sqrt[1 + x]), x];
FullSimplify[rubiSol == mathSol]
(* True *)

It produces the same result as Mathematica and can provide a list of steps: