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Exercise

∫−x2x2(log(2+sint))dt\int_{-x^2}^{x^2}\left(log\left(2+sint\right)\right)dt

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Final answer to the exercise

(sin⁡(x2)+2)ln⁡∣sin⁡(x2)+2∣−sin⁡(x2)−2ln⁡∣10∣+−sin⁡(x2)+2+ln⁡∣−sin⁡(x2)+2∣sin⁡(x2)−2ln⁡∣−sin⁡(x2)+2∣ln⁡∣10∣\frac{\left(\sin\left(x^2\right)+2\right)\ln\left|\sin\left(x^2\right)+2\right|-\sin\left(x^2\right)-2}{\ln\left|10\right|}+\frac{-\sin\left(x^2\right)+2+\ln\left|-\sin\left(x^2\right)+2\right|\sin\left(x^2\right)-2\ln\left|-\sin\left(x^2\right)+2\right|}{\ln\left|10\right|}

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∫−x2x2(log(2+sint))dt
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