Posted by **M** on Sunday, March 18, 2007 at 10:52pm.

Hi. How can I integrate 1/(X^3 +1) ? Thank you to anyone who can help me :-)

Write 1/(x^3 +1) as

1/[(x+1)(x^2-x+1)]

Then use integration by parts, letting

dv = dx/(x^2 -x +1)

u = 1/(x+1)

du = log (x+1)

v = (2/sqrt3)arctan[(2x-1)/sqrt3]

That should take you to the answer. I know what the answer is (from my table of integrals), but have not done all the steps.

Could you by any chance tell me what your table of integrals says. I can't find it on mine to check my answer

OK. The answer is

(1/3){(1/2)log[(x+1)^2/(x^2-x+1)] + sqrt3*arctan[(2x-1)/sqrt3]}

Quite a mess. My approach does seem to lead to that answer.

## Answer This Question

## Related Questions

- calculus-integration - integrate -2/xln^4(x)...plz help me..give me an idea on ...
- calculus-integration! - should i use substitution?? if yes how should should i ...
- Calculus - I have to use integration by parts to integrate tan^-1 (1/x)dx. I'm ...
- Integral calculus - Please can anyone help with the following problems - thanks...
- Calculus - How do I integrate (x^2)(e^(x^3)) dx? I think it is integration by ...
- calculus - How do I integrate x(arctanx) dx? Is it some sort of integration by ...
- Integration by parts - integrate (e^x-x)^2 dx
- integrate - how do i integrate 2u du /u-2+2u^2 so i used subsitution rule? or ...
- Calculus - Explain how you would use the power integration formula to integrate ...
- Calculus II - Integrate using integration by parts (integral) (5-x) e^3x u = 5-x...

More Related Questions