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

e∫^P(x)

∫[itex]\frac{x-2}{x(x-1)}[/itex]dx

3. The attempt at a solution

so i split it into

∫[itex]\frac{x-2}{x(x-1)}[/itex]dx

= ∫[itex]\frac{2x-1}{x^2-x}[/itex]dx - ∫[itex]\frac{x+1}{x^2-x}[/itex]dx

= ln(x^{2}-x) - ∫[itex]\frac{x}{x^2-x}[/itex] - ∫(x^{2}-x)^{-1}

= ln(x^{2}-x) - ln(x-1) -∫(x^{2}-x)^{-1}

ok. having problems working out ∫(x^{2}-x)^{-1}dx

tried many ways but i keep ending up with the original integral.

u=x^{-1}--> du=-x^{-2}

dv= (x-1)^{-1}dx --> v=ln(x-1)

gives me ([itex]\frac{1}{x}[/itex])ln(x-1) + ∫[itex]\frac{ln(x-1)}{x^2}[/itex]dx

when i work this out

∫[itex]\frac{ln(x-1)}{x^2}[/itex]dx

u=ln(x-1) --> du=[itex]\frac{1}{x-1}[/itex]

dv=x^{-2}dx --> v=-x^{-1}

i get

∫[itex]\frac{ln(x-1)}{x^2}[/itex]dx = [itex]\frac{-ln(x-1)}{x}[/itex] +∫(x^{2}-x)^{-1}

which is the same integral and above and i get no solution.

Need help......

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# Integrating Factor Differential Equation

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