i'm trapped with a problem: [tex]\int\frac{dx}{x\sqrt{2-x-x^2}}[/tex].(adsbygoogle = window.adsbygoogle || []).push({});

i think this problem could be solved by subtitutions: [tex]\ x+\frac{1}{2}=\frac{3}{2}sint[/tex] and [tex]\ u=tan\frac{t}{2}[/tex].

and finally we would get an expression in [tex]\ u[/tex]: [tex]\frac{\sqrt{2}}{4} log\left|\frac{2\sqrt{2}+u-3}{2\sqrt{2}-u+3}\right|[/tex]

(am i right so far?)

however i find it difficult and tedious to write the result in x and get the final answer.

does anyone know how to evaluate this integral in an alternative way?

Thanks a lot.

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# Integrals of rational functions

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