Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

Possible Duplicate:
Evaluating this integral for different values of a constant

Is there a solution to the definite integral, $$\int\limits_{0}^{\infty} \frac{1}{x^{\frac{1}{n}}}\frac{1}{1+x^2}\mathrm{d}x$$ where, $n \in \mathbb{N}$

HINT : substitute, $x = \tan\theta$

share|cite|improve this question

marked as duplicate by joriki, martini, Asaf Karagila, Did, t.b. Aug 11 '12 at 9:11

This question was marked as an exact duplicate of an existing question.

Are you giving us a hint ? – Belgi Aug 11 '12 at 7:12
I wonder if there's something special about $n\in\Bbb N$ and $x=\tan\theta$ that makes this question seek a different type of answer than the one given in the duplicate question. – anon Aug 11 '12 at 7:25

Maple says that $$\int\limits_0^{\infty}x^{-1/n}\dfrac 1{x^2+1}dx=\dfrac 12\pi\sec\left(\dfrac{\pi}{2n}\right)$$

share|cite|improve this answer

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