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I want to evaluate an indefinite integral using the Integrate command, and I know that the answer can be written in terms of elementary functions (square roots, logs etc.) but Mathematica seems to give the answer in terms of a Hypergeometric2F1 function. How do I get it to give me the answer in terms of the elementary functions?

The integral is the following: $$ \int \sqrt{\left(\frac{w}{2}\right)\left(\frac{w}{2}+u+v\right)} \ \mathrm{d}w $$


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closed as off-topic by Daniel Lichtblau, bobthechemist, belisarius, RunnyKine, Michael E2 Aug 13 '14 at 23:06

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – Daniel Lichtblau, belisarius, RunnyKine, Michael E2
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What are u and v, constants or functions? If the former then it doesn't yield Hypergeometric2F1 but an elementary expression involvig square roots and logarithms. You should provide your original input if you expect any help. –  Artes Aug 13 '14 at 21:32
Please restart your Mathematica session and try again.You probably have some lingering definition for u and/or v –  belisarius Aug 13 '14 at 22:16
I realized that I was using (0.5) for the square root's power, but using (1/2) gave the correct answer! –  Sheheryar Zaidi Aug 13 '14 at 22:33

1 Answer 1

No apparent complication in v10 under Windows:

Integrate[Sqrt[w/2 (w/2 + u + v)], w]
(Sqrt[w] Sqrt[2 u + 2 v + w] (Sqrt[w] (u + v + w) Sqrt[2 u + 2 v + w] - 2 ((u + v)^2) 
  Log[Sqrt[w] + Sqrt[2 u + 2 v + w]]))/(4 Sqrt[w (2 u + 2 v + w)])
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Same result on v9 –  belisarius Aug 13 '14 at 22:15

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