Biến đổi:
$\int\limits f(x)đx=\int\limits \frac{dx}{\tan x\cos^4x} $
Đặt $t=\tan x$ suy ra:
$dt=\frac{dx}{\cos^2x} $ & $\frac{dx}{\tan x\cos^4x}=\frac{1}{\tan x} (1+\tan^2x)\frac{dx}{\cos^2x}=\frac{(1+t^2)dt}{t}=(\frac{1}{t}+t)dt $
Khi đó:
$\int\limits f(x)dx=\int\limits (\frac{1}{t}+t)dt=\ln|t|+\frac{1}{2}t^2+C=\ln|\tan x|+\frac{1}{2}\tan^2x+C $