(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the integral of x over ((1+x)^{1/2}-(1+x)^{1/3}) dx

2. Relevant equations

integration by substitution.

3. The attempt at a solution

I have tried the substitution u = (1+x)^{5/6}but not really sure if this makes it any better!

du/dx = 5/6 * (1+x)^{-1/6}

6/5 * du = (1+x)^{-1/6}dx

(1+x) = u^{6/5}

x= u^{6/5}- 1

Take a factor of (1+x)^{1/6}of the denominator and rewrite to give:

6/5 * integral of (u^{6/5}- 1)/(u^{2/5}- u^{1/5}) du

Is is possible to integrate this? Or do I need a completely different substitution?

Thanks.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Integration- is it possible to integrate this?

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