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\frac{1}{4}\int_{0}^{1} \frac{1+x}{1+2x} \frac{\ln(x)}{\sqrt{x-x^2}}dx - \int_{0}^{+\infty}\frac{\ln\big(\cos^2(x)\big)\sin^3(x)}{x^3(1+2\cos^2(x))}
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