1. Integration

Hi

How exactly do I integrate t^2/(t^4+1) without using partial fractions (cause that looks soooo complicated)?

PS I got that after using the t method trying to integrate 1/((cosx)^2+1)

2. Originally Posted by xwrathbringerx
Hi

How exactly do I integrate t^2/(t^4+1) without using partial fractions (cause that looks soooo complicated)?

PS I got that after using the t method trying to integrate 1/((cosx)^2+1)
$\displaystyle \int{\frac{t^2}{t^4 + 1}\,dt}$

http://www.wolframalpha.com/input/?i=integral[%28x^2%29%2F%28x^4+%2B+1%29]

Click "Show Steps".

3. Ummm the computer uses partial fractions but I dont think i am capable of figuring such long denominators out during the exam...is there another way?

4. Originally Posted by xwrathbringerx
Ummm the computer uses partial fractions but I dont think i am capable of figuring such long denominators out during the exam...is there another way?
I'd say there isn't - the computer probably wouldn't resort to partial fractions unless absolutely necessary.

5. Originally Posted by xwrathbringerx
Hi

How exactly do I integrate t^2/(t^4+1) without using partial fractions (cause that looks soooo complicated)?

PS I got that after using the t method trying to integrate 1/((cosx)^2+1)
$\displaystyle \int \frac{t^2}{t^4+1} dt = \int \left( \sum_{n=0}^{\infty} (-1)^n t^{4n+2} \right) dt$.