HI , can anyone give me a way to solve :

$\displaystyle

\int \frac{x^2}{1+x^4}dx

$

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- Jun 12th 2010, 10:35 AMparkhidLooks Simple Integral But it is fake
HI , can anyone give me a way to solve :

$\displaystyle

\int \frac{x^2}{1+x^4}dx

$ - Jun 12th 2010, 11:03 AMwonderboy1953Thought
I'm considering multiply both top and bottom by $\displaystyle x^{-2}$, then let $\displaystyle x = e^u$ which I believe converts to a familiar function (but you may also have to integrate by parts).

- Jun 12th 2010, 11:41 AMchiph588@
- Jun 12th 2010, 01:10 PMAckbeet
You can also use complex line integration. See here for a very similar sort of integral.

- Jun 12th 2010, 01:18 PMchisigma
There is only a minor detail: the integral proposed by parkhid is

*indefinite*and its solution is a family of functions... the integral of Your example is*definite*and its solution [if it exists...] is a real [or complex] number...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$ - Jun 12th 2010, 01:26 PMAckbeet
Very true. My bad.