Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

There's an integral I've no idea how to solve. Even Wolfram|Alpha gives a very odd result.
$$\int \frac{\sqrt{1 - x^2} + \sqrt{1 + x^2}}{\sqrt{1 - x^4}}dx$$

share|cite|improve this question
What have you tried? Where did you get stuck? Where is this problem from? Did you notice that $1-x^4 = (1-x^2)(1+x^2)$? – Fixee Apr 10 '11 at 19:07
up vote 20 down vote accepted

Have you tried to take apart the integrand into two fractions? This immediately gives $$\int \left( \frac{1}{\sqrt{1 + x^2}} + \frac{1}{\sqrt{1 - x^2}} \right) \, dx = \sinh^{-1} (x) + \sin^{-1} (x) + C.$$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.