How do I solve this integral?

$$\int\limits_{-\infty}^{0} \frac{x^{2}}{9 + x^{6}}dx$$

I have tried trig sub but it is really ugly.

I assume by completing the square but the answer is pi/9

Question

How do I solve this integral?

$$\int\limits_{-\infty}^{0} \frac{x^{2}}{9 + x^{6}}dx$$

I have tried trig sub but it is really ugly.

I assume by completing the square but the answer is pi/9

anonymous · Answer

its an improper integral

australopithecus · Answer

note that I took this integral from 

$$\int\limits\limits\limits_{-\infty}^{\infty} (x^{2}/(9 + x^{2}))dx$$

australopithecus · Answer

oh crud I wrote it wrong

anonymous · Answer

you have to set up the limit as x approaches infinity of that integral from t to 0 instead of infinity to 0

australopithecus · Answer

|dw:1336097338927:dw|

australopithecus · Answer

yeah I know this question is in regards to finding the integral of this function

turingtest · Answer

you can long-divide, then use partial fractions

turingtest · Answer

oh that's a six in the bottom?!?

turingtest · Answer

did I rewrite it correctly?

blockcolder · Answer

Let u=x^3.

turingtest · Answer

^yep

blockcolder · Answer

It will become arctan(something).

anonymous · Answer

you could make it a product and use int by parts

turingtest · Answer

that would be a huge mess

anonymous · Answer

you could derive a quotient rule base integration formula in the same way you get the int by parts one :P

australopithecus · Answer

the integral is

$$\int\limits_{-\infty}^{\infty} x^{2}dx/(9+x^{6})$$

australopithecus · Answer

trig sub also seems hopeless :\

blockcolder · Answer

Have you tried letting u=x^3 to get rid of the x^2 on top?

anonymous · Answer

okay maybe we have to evaluate the riemann sum

australopithecus · Answer

yeah that seems like the best way to solve it :)