Integration: 1/((x^(1/2)-x^(1/3))

[Bohn507]

I have no idea where to start with this. Sorry about the format, I don't know where to make it into an easier to read style.

1/((x^(1/2)-x^(1/3))

 

[GRFrones]

The problem is: $\int \dfrac{1}{\sqrt{x} - \sqrt[3]{x}} dx$

Here, http://www.wolframalpha.com/input/?i=integrate+1%2F((x^(1%2F2)-x^(1%2F3))
Click on show steps and that's it.

See LaTeX for formatting your equations here.

 

[Bohn507]

Thank you!

 

[arildno]

Or, you could do as follows:
Introduce:
$$x=u^{6}\to\frac{dx}{du}=6u^{5}\to{dx}=6u^{5}du$$
Then,
$$\int\frac{dx}{\sqrt{x}-\sqrt[3]{x}}=\int\frac{6u^{5}}{u^{3}-u^{2}}du=\int\frac{6u^{3}}{u-1}du=6\int({u}^{2}+u+1+\frac{1}{u-1})du$$
which is easily integrated.