2
$\begingroup$

I've just got my hands on Wolfram Mathematica and tried to see if I can figure out how to use it by myself. I've plugged in an integral $\int \frac{dx}{(1-x^2)^{2/3}}$, knowing that the result is $\frac{x}{\sqrt{1-x^2}}$. But Mathematica gave me something different:

In[10]:= Integrate[1/((1-x^2)^(2/3)), x]
Out[10]:= x Hypergeometric2F1[1/2,2/3,3/2,x^2]

What does this mean and what am I doing wrong?

Improve this question
$\endgroup$

1 Answer 1

Reset to default
4
$\begingroup$

This is more a long comment than an answer.

If you calculate:

D[x Hypergeometric2F1[1/2, 2/3, 3/2, x^2], x]
FullSimplify@D[x/Sqrt[1 - x^2], x]

You find respectively:

1/(1 - x^2)^(2/3)

and

1/(1 - x^2)^(3/2)

Mathematica gives the correct answer: Check the exponents!!

Improve this answer
$\endgroup$
2
  • 1
    $\begingroup$ Umm. Jeez. I'm so stupid. $\endgroup$
    – Akiiino
    Commented Jan 31, 2016 at 8:38
  • 1
    $\begingroup$ No. Your mistake is common. I've seen it made by plenty of people ranging from highschool students to engineering/science professors at good universities. You, like me, were probably taught calculus by people who had little experience with it in the real world. You were taught to expect that there is a "correct" answer to the integral. Instead you should have investigated whether the solution had the properties of a correct solution. $\endgroup$
    – Searke
    Commented Jan 31, 2016 at 23:45

Not the answer you're looking for? Browse other questions tagged or ask your own question.