\int\frac{\sqrt{1-x^{2}}-x}{x^{3}-x^{2}-x+1-\sqrt{1-x^{2}}+x\sqrt{1-x^{2}}}dx
It is not as tough as it looks ;)
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3 Answers
62of course not! (I have even disallowed all the best TIIT users :P )
I only post for the general aspirant :) (unless otherwise mentioned :D
106\int \frac{\sqrt{1-x^2}-x}{(x-1)(x^2-1+\sqrt{1-x^2})}dx
\int \frac{(\sqrt{1-x^2}-1)+(1-x)}{(x-1)\sqrt{1-x^2}(1-\sqrt{1-x^2})}dx
splitting
-\int \frac{1}{(x-1)\sqrt{1-x^2}}+\frac{1}{\sqrt{1-x^2}-(1-x^2)}
now it should be able to be solved