[tex]\int \frac{cosxdx}{4cos^{3}x-3cosx}=\int \frac{dx}{4cos^{2}x-3}[/tex] [tex]=\int \frac{\frac{1}{cos^{2}x}dx}{4-\frac{3}{cos^{2}x}}[/tex]
Đặt [tex]t=tanx\Rightarrow \frac{3}{cos^{2}x}=3(1+t^2);dt=\frac{dx}{cos^{2}x}[/tex]
[tex]\Rightarrow I=\int \frac{dt}{4-3(1+t^2)}=\int \frac{dt}{1-3t^2}=\frac{1}{2}\int \left ( \frac{1}{\sqrt{3}.t+1}-\frac{1}{\sqrt{3}.t-1} \right )dt[/tex]
[tex]=\frac{1}{2\sqrt{3}}ln\left | \frac{\sqrt{3}t+1}{\sqrt{3}t-1} \right |+C=\frac{1}{2\sqrt{3}}ln\left | \frac{\sqrt{3}.tanx+1}{\sqrt{3}.tanx-1} \right |+C[/tex]
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
