# Calculus

posted by M

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

(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.

## Similar Questions

1. ### Integral calculus

Please can anyone help with the following problems - thanks. 1) Integrate X^4 e^x dx 2) Integrate Cos^5(x) dx 3) Integrate Cos^n(x) dx 4) Integrate e^(ax)Sinbx dx 5) Integrate 5xCos3x dx The standard way to solve most of these integrals …
2. ### calculus-integration!

should i use substitution?? if yes how should should i use it?
3. ### calculus-integration

integrate -2/xln^4(x)...plz help me..give me an idea on how to start..plz The derivative of the ln(x) function is 1/x and this is multiplying the ln^4(x). You can thus write the integral as: -2 * 1/5 ln^5(x) + constant. is that the …
4. ### integrate

how do i integrate 2u du /u-2+2u^2 so i used subsitution rule?
5. ### Calculus

Explain how you would use the power integration formula to integrate the function f(x) = (1/x^2)-(1/x)+(1/4).
6. ### Integration by parts

integrate (e^x-x)^2 dx
7. ### Calculus

How do I integrate (x^2)(e^(x^3)) dx? I think it is integration by parts but after trying that, I got confused?
8. ### calculus

How do I integrate x(arctanx) dx? Is it some sort of integration by parts?
9. ### Calculus

I have to use integration by parts to integrate tan^-1 (1/x)dx. I'm not sure what to use as u or dv. We were taught to use uv-integral of (vdu) to do this.
10. ### Calculus II

Integrate using integration by parts (integral) (5-x) e^3x u = 5-x du = -dx dv = e^3x v = 3e^3x I wonder if this is right so far. = uv - (integral) v du = (5-x)(3e^3x) - (integral) (-3e^3x) =(5-x)(3e^3x) + (integral) (3e^3x) = (5-x)(3e^3x) …

More Similar Questions