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Find the value of this integration

Source: 2019 Jozsef Wildt International Math Competition-W. 6

May 18, 2020
integrationtrigonometrylogarithmscalculus

Problem Statement

Compute∫π6π4(1+ln⁡x)cos⁡x+xsin⁡xln⁡xcos⁡2x+x2ln⁡2xdx\int \limits_{\frac{\pi}{6}}^{\frac{\pi}{4}}\frac{(1+\ln x)\cos x+x\sin x\ln x}{\cos^2 x + x^2 \ln^2 x}dx
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