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Question Number 132414 by john_santu last updated on 14/Feb/21

Commented by john_santu last updated on 14/Feb/21

$$\underset{―}{\mathrm{super}\mathrm{nice}\mathrm{integral}}$$

Answered by liberty last updated on 14/Feb/21

$$-{\int }_2^4\frac{{(1-{\cos }^2\mathrm{x})}^2}{\cos \mathrm{x}}\mathrm{d}\left(\cos \mathrm{x}\right)=$$$$-\int \frac{1-2\cos {}^2\mathrm{x}+\cos {}^4\mathrm{x}}{\cos \mathrm{x}}\mathrm{d}\left(\cos \mathrm{x}\right)=$$$$-{\{\ln \mid \cos \mathrm{x}\mid -\cos {}^2\mathrm{x}+\frac{1}{4}\cos {}^4\mathrm{x}\}}_2^4=$$$$-\{\ln \mid \frac{\cos 4}{\cos 2}\mid -(\cos {}^2\left(4\right)-\cos {}^2\left(2\right))+\frac{1}{4}[\cos {}^4\left(4\right)-\cos {}^4\left(2\right)]\}$$

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