bai toan tich phan..

  • Thread starter truongthilien5
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nguyenbahiep1

$I = \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{e^{3x}}{cos^2x(1+e^{3x})}dx \\ \\ I = \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{e^{3x}+1- 1}{cos^2x(1+e^{3x})}dx \\ \\ I = \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\frac{dx}{cos^2x} - \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\frac{dx}{cos^2x(1+e^{3x})} = I_1 - I_2 \\ \\ I_2 : x = - t \Rightarrow I_2 = \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\frac{e^{3t}dt}{cos^2t(1+e^{3t})} = I \\ \\ I = tanx \big|_{-\frac{\pi}{4}}^{\frac{\pi}{4}} - I \\ \\ \Rightarrow I = \frac{1}{2} tanx \big|_{-\frac{\pi}{4}}^{\frac{\pi}{4}} = ?$
 
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