Integrate 1/(2x+2x^2): Step-by-Step Guide

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Homework Statement


int(1/(2x+2x^2))dx


The Attempt at a Solution


can someone help me where to start with this one i know its not hard, but i can't find out what to factorize then do parts??

ive forgotten this simple integration stuff, do i make it 1/2x(x+1) then integrate by parts?? anyways the answer is -(1/2)ln(x+1)+(1/2)ln(x) i have to use parts don't i, or can i separate some how??
 
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Since you've factorized the denominator, seems like you should integrate by partial fractions, not by parts.
 
ah ok ty, let me try
 
lol ty for pointing how stupid i can be sometimes... quite embarrassing lol
 
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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