Integration by substitution question

Question: Find the integral of

\displaystyle\int^8_1 \dfrac{1}{x(1+ \sqrt[3]{x})}\ dx

using the substitution x = u³. I'm stuck at a step.

Here's how I tried to do it:
dx = 3u² x du

\Rightarrow \displaystyle\int^2_1 \dfrac{1}{u^3(1+ \sqrt[3]{u^3})}\ 3u^2 \times du

\Rightarrow 3\displaystyle\int^2_1 \dfrac{1}{u(1+ u)}\ du

I don't know how to do it after that! Any help would be appreciated.

Split it into partial fractions :

A/u + B/(1+u) = 1/u(1+u)

Can you do it now ?

Original post by Ari Ben Canaan

Split it into partial fractions :

A/u + B/(1+u) = 1/u(1+u)

Can you do it now ?

Oops, I should've thought more on this question. Yes, I can do it now.
-Thanks

(edited 12 years ago)

Student story: studying for a career in law

Why I loved studying online

How to save (and earn) more money while you're at university

What university is really like