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

  • Thread starter Bohn507
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  • #1
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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))
 

Answers and Replies

  • #2
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The problem is: [itex]\int \dfrac{1}{\sqrt{x} - \sqrt[3]{x}} dx[/itex]

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.
 
  • #3
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Thank you!
 
  • #4
arildno
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Or, you could do as follows:
Introduce:
[tex]x=u^{6}\to\frac{dx}{du}=6u^{5}\to{dx}=6u^{5}du[/tex]
Then,
[tex]\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[/tex]
which is easily integrated.
 

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