# An integral

• December 19th 2008, 12:54 AM
Kamikazi
An integral
How would you to integrate:
1/[x^2* ((1+x^3)^(2/3))]
Thanks(Nod)
• December 19th 2008, 12:59 AM
Chop Suey
Use a reciprocal substitution such as $u=\frac{1}{x}$
• December 19th 2008, 03:20 AM
Kamikazi
Quote:

Originally Posted by Chop Suey
Use a reciprocal substitution such as $u=\frac{1}{x}$

I 've tried this way before but it seems to be not effective.(Headbang)
Could you solve it more detailed?
Thanks (Nod)
• December 19th 2008, 03:41 AM
Chop Suey
$\int \frac{1}{x^2(1+x^3)^{\frac{2}{3}}}~dx$

Subbing $u = \frac{1}{x} \implies du = -\frac{1}{x^2}~dx$ switches the integral to:
$-\int \frac{1}{(1+\frac{1}{u^3})^{\frac{2}{3}}}~du=-\int \frac{1}{(\frac{u^3+1}{u^3})^{\frac{2}{3}}}~du = -\int \frac{u^2}{(u^3+1)^{\frac{2}{3}}}~du$

You should pick this up right away.