How can completing the square help simplify the integral (1+x)/(1-x-x^2) dx?

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Homework Statement


this is LFS of a question,which is
(1+x)/(1-x-x^2) dx!
i can not simplefy it at all b4 try to do d integration!

Homework Equations





The Attempt at a Solution

 
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Try completing the square for 1-x-x2. Your integral is in the form (a+b)/c which is the same as (a/c) + (b/c), so split the integrals.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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