Why can't Mathematica solve this definite integral?

问题

When I try to calculate the following integral in Mathematica 8, I get this strange result:

In[1]:= Integrate[y/((1 + x^2 + y^2)^(3/2)), {y, 0, 1}]

Maple 14 can solve this one easily:

Why is Mathematica giving me a different result?

回答1:

Try this

r = Integrate[y/((1 + x^2 + y^2)^(3/2)), {y, 0, 1}]
r = Assuming[Element[x, Reals], Simplify[r]];
Together[r]

which gives

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

Which is the same as Maple's :

来源：https://stackoverflow.com/questions/8692674/why-cant-mathematica-solve-this-definite-integral