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Help me please with integral: $\int \frac{2x-\sqrt{4x^{2}-x+1}}{x-1}\;dx$

I must solve it without using Euler substitution.

Thanks!

  • 0
    Is it solvable by Euler substitution? I can't solve it at all...2012-01-31

1 Answers 1

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Hint: writing $\frac{2x-\sqrt{4x^2-x+1}}{x-1}=\frac{2x-\sqrt{4x^2-x+1}}{x-1}\frac{2x+\sqrt{4x^2-x+1}}{2x+\sqrt{4x^2-x+1}},$ we find $\frac{2x-\sqrt{4x^2-x+1}}{x-1}=\frac{4x^2-(4x^2-x+1)}{(x-1)(2x+\sqrt{4x^2-x+1})}=\frac 1{2x+\sqrt{4x^2-x+1}}.$

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    @lewist: Yes, it ruins. I am not able to find a new valid solution.2012-01-28