Tích phân

N

nguyenbahiep1

câu 1

[laTEX]I = \int_{0}^{\frac{\pi}{4}} \frac{dx}{cos^2x(tan^2x - 3)} \\ \\ tan x = u \\ \\ I = \int_{0}^{1} \frac{du}{u^2-3} \\ \\ I = \frac{1}{2\sqrt{3}}(\frac{du}{x-\sqrt{3}} - \frac{du}{x+ \sqrt{3}}) \\ \\ I =\frac{1}{2\sqrt{3}} ln|\frac{x-\sqrt{3}}{x+\sqrt{3}}| \big|_0^1 =\frac{1}{2\sqrt{3}} ln |\sqrt{3}-2| [/laTEX]
 
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