Issue in Hard Integral

[mariuszi28cg]

I tried:

Int[((x^2 - 2)*Exp[x])/((x - 1)*Sqrt[1 - x^2]), x]

give me:

Int[E^x/Sqrt[1 - x^2], x] + Int[E^x/((1 - x) Sqrt[1 - x^2]), x] +
Int[(E^x x)/Sqrt[1 - x^2], x]

but the answer is: (E^x (1 + x))/Sqrt[1 - x^2]

Mathematica can't compute it's very strange. Maple can.

Thanks.

[stblake]

This is a good integral for the rational part of Bronstein's algorithm.

-- Rubi does not have a rule for this type of integral.

-- Mathematica does not implement Bronstein's algorithm for the mixed transcendental/algebraic case of the Risch algorithm.