I set u=x^{1/3} and 3u^{2} du = dx

u^3 = x

I make a devision and get

With the last term I am not sure what to do.

I do integration by parts and get

and the integral then

and my solution

And then I would put back u=x^{1/3}

But the answer should be

I am cannot figure out where I go wrong.

Thanks for any help.