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Solve this integration from Jozsef competition 2019

Source: 2019 Jozsef Wildt International Math Competition-W. 3

May 18, 2020
integrationtrigonometrycalculus

Problem Statement

Compute ∫−π4π4cos⁡x+1−x2(1+xsin⁡x)1−x2dx\int \limits_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\frac{\cos x+1-x^2}{(1+x\sin x)\sqrt{1-x^2}}dx
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