Tích phân hàm số toán tangent

$\int \tan axdx=-\frac{1}{a}\ln |\cos ax|+C=\frac{1}{a}\ln |\sec ax|+C$

$\int {\tan }^{n}axdx=\frac{1}{a(n-1)}{\tan }^{n-1}ax-\int {\tan }^{n-2}axdx\text{(for }n\ne 1\text{)}$

$\int \frac{dx}{q\tan ax+p}=\frac{1}{p^2+q^2}(px+\frac{q}{a}\ln |q\sin ax+p\cos ax|)+C\text{(for }{p}^2+q^2\ne 0\text{)}$

$\int \frac{dx}{\tan ax}=\frac{1}{a}\ln |\sin ax|+C$

$\int \frac{dx}{\tan ax+1}=\frac{x}{2}+\frac{1}{2a}\ln |\sin ax+\cos ax|+C$

$\int \frac{dx}{\tan ax-1}=-\frac{x}{2}+\frac{1}{2a}\ln |\sin ax-\cos ax|+C$

$\int \frac{\tan axdx}{\tan ax+1}=\frac{x}{2}-\frac{1}{2a}\ln |\sin ax+\cos ax|+C$

$\int \frac{\tan axdx}{\tan ax-1}=\frac{x}{2}+\frac{1}{2a}\ln |\sin ax-\cos ax|+C$