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Question Number 167609 by peter frank last updated on 20/Mar/22

Answered by MJS_new last updated on 20/Mar/22

∫((1−x^2 )/((x−2x^2 )))dx=∫((1/2)+(1/x)−(3/(2(2x−1))))dx=  =(x/2)+ln ∣x∣ −(3/4)ln ∣2x−1∣ +C

$$\int\frac{\mathrm{1}−{x}^{\mathrm{2}} }{\left({x}−\mathrm{2}{x}^{\mathrm{2}} \right)}{dx}=\int\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{{x}}−\frac{\mathrm{3}}{\mathrm{2}\left(\mathrm{2}{x}−\mathrm{1}\right)}\right){dx}= \\ $$$$=\frac{{x}}{\mathrm{2}}+\mathrm{ln}\:\mid{x}\mid\:−\frac{\mathrm{3}}{\mathrm{4}}\mathrm{ln}\:\mid\mathrm{2}{x}−\mathrm{1}\mid\:+{C} \\ $$

Commented by peter frank last updated on 21/Mar/22

thank you

$$\mathrm{thank}\:\mathrm{you} \\ $$

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