Question

Integrate.
integral (x^1/3/x^2/3(1+x^1/3))dx

Answer 1

\[\int\limits (\frac{ x^{1\frac{ 1 }{ 3 }} }{ x^{\frac{ 2 }{ 3 }}(1+x^{\frac{ 1 }{ 3 }}) })dx\]

Answer 2

whoops that extra 1 on the top should be there.
i set u = 1+x^1/3

Answer 3

oops, i meant that extra 1 shouldn't be there.

du = 1/3x^-2/3
so the new integral should be
\[\int\limits (\frac{ u+1 }{ u })du\]
right?

Answer 4

\[\int\frac{x^{\frac{1}{3}}}{x^{\frac{2}{3}}\left(1+x^{\frac{1}{3}}\right)}\;dx\\
\begin{align*}\text{Letting } u&=1+x^{\frac{1}{3}}\\
du&=\frac{1}{3}x^{-\frac{2}{3}}\;dx\end{align*}\\
3\int\frac{u-1}{u}\;du\]
Close, though!

Answer 5

yeah i realized i typed my response wrong.
yeah the top should be u -1 and there should be a 3 in the front.
after i deleted my old response i forgot.

Answer 6

The integral is much simpler here; think you can manage?

Answer 7

yeah i think so.
thanks :)