CODEWITHSUNDEEP
wolfram-mathematicaintegral
Martin Koller
Martin Koller

Reputation: 115

Why can't Mathematica solve this definite integral?

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}]

Mathematica graphics

Maple 14 can solve this one easily:


Why is Mathematica giving me a different result?

Upvotes: 8

Views: 5640

Answers (1)

Nasser
Nasser

Reputation: 13181

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 :

enter image description here

Upvotes: 12

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