How would you to integrate:

1/[x^2* ((1+x^3)^(2/3))]

Thanks(Nod)

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- Dec 19th 2008, 12:54 AMKamikaziAn integral
How would you to integrate:

1/[x^2* ((1+x^3)^(2/3))]

Thanks(Nod) - Dec 19th 2008, 12:59 AMChop Suey
Use a reciprocal substitution such as $\displaystyle u=\frac{1}{x}$

- Dec 19th 2008, 03:20 AMKamikazi
- Dec 19th 2008, 03:41 AMChop Suey
$\displaystyle \int \frac{1}{x^2(1+x^3)^{\frac{2}{3}}}~dx$

Subbing $\displaystyle u = \frac{1}{x} \implies du = -\frac{1}{x^2}~dx$ switches the integral to:

$\displaystyle -\int \frac{1}{(1+\frac{1}{u^3})^{\frac{2}{3}}}~du=-\int \frac{1}{(\frac{u^3+1}{u^3})^{\frac{2}{3}}}~du = -\int \frac{u^2}{(u^3+1)^{\frac{2}{3}}}~du $

You should pick this up right away.