10
$\begingroup$

I have been working on the indefinite integral of $\cos x/(1+x^2)$.

$$ \int\frac{\cos x}{1+x^2}\;dx\text{ or } \int\frac{\sin x}{1+x^2}\;dx $$

are they unsolvable(impossible to solve) or is there a way to solve them even by approximation?

Thank you very much.

  • 2
    wolfram alpha provides a [solution](http://www.wolframalpha.com/input/?i=Integrate%5BCos%5Bx%5D%2F%281+%2B+x%5E2%29%2C+x%5D) in terms of sine and cosine-integrals.2012-04-09
  • 0
    Why is the word "undefined" in the title?2012-04-09
  • 0
    By maple and matlab also you can get the solution in terms of cosine and sine but i want to know if there is exact solution or the way for it?2012-04-09
  • 0
    Please define what exactly you mean by "unsolvable".2012-04-09
  • 1
    I do not believe "impossible to solve" is a definition in the sense of @Aryabhata. Why do you not accept the solution in terms of sine and cosine-integral as being a solution? What would be a solution for you?2012-04-09
  • 0
    A friend of mine told me that [$\int e^{ix}/(1+x^2)dx=...$](http://tinyurl.com/cppbp4x) Does this help you?2012-05-09
  • 1
    I guess there is no explicit formula for the indefinite integral. I know and estimate $$ \int_{0}^{\pi/2}\frac{\cos x}{1+x^2}\;dx\ge \int_{0}^{\pi/2}\frac{\sin x}{1+x^2}\;dx $$2012-04-09
  • 2
    Defacing your questions is quite frowned upon; please don't do this.2013-03-27

2 Answers 2