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

Express recurrence relation of the integral

$$ I_n=\int\frac{dx}{(1+x^2)^n} $$

[My Answer]

$$ I_n = \int\frac{1+x^2}{(1+x^2)^n}dx-\int\frac{x^2}{(1+x^2)^n}dx $$

$$ I_n=I_{n-1}-\int x\cdot\frac{x}{(1+x^2)^n}dx $$

$$ I_n=I_{n-1}-\frac{x}{2(1-n)(x^2+1)^{n-1}}+\frac{1}{2(1-n)}I_{n-1} $$

$$ I_n=\frac{2n-3}{2(n-1)}I_{n-1}+\frac{x}{2(n-1)(x^2+1)^{n-1}} \ \ \ \ (n>1) $$

$$ I_1=\arctan(x) $$

Is my answer correct?

share|cite|improve this question
The answer you got is correct. – André Nicolas Oct 31 '12 at 12:06

Yes, the answer is correct (up to a constant, but it does not not change the idea).

share|cite|improve this answer

Your Answer


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

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