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

[itex]\int[/itex][itex]\frac{dx}{x-\sqrt{1-x^2}}[/itex]

2. Relevant equations

3. The attempt at a solution

i try to simplify it by multiplying [itex]\frac{x+\sqrt{1-x^2}}{x+\sqrt{1-x^2}}[/itex],becoming =[itex]\frac{x+\sqrt{1-x^2}}{2x^2-1}[/itex]

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

ps:

a.Can i partial fraction the last term to [itex]\frac{A}{x-\frac{1}{\sqrt{2}}}[/itex]+[itex]\frac{B}{x+\frac{1}{\sqrt{2}}}[/itex]??

b.i try to integrate by using wolfram alpha online ,but the steps is incredibly long..:yuck:

does it exist any other simpler way??

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# Homework Help: Integral of 1/{x-(1-x^2)0.5}

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