Tích phân hàm số toán cosine

$\int {\cos }^{n}axdx=\frac{{\cos }^{n-1}ax\sin ax}{na}+\frac{n-1}{n}\int {\cos }^{n-2}axdx\text{(for }n>0\text{)}$

$\int x\cos axdx=\frac{\cos ax}{a^2}+\frac{x\sin ax}{a}+C$

$\int {\cos }^{2}axdx=\frac{x}{2}+\frac{1}{4a}\sin 2ax+C=\frac{x}{2}+\frac{1}{2a}\sin ax\cos ax+C$

$\int x^2{\cos }^{2}axdx=\frac{x^3}{6}+(\frac{x^2}{4a}-\frac{1}{8a^3})\sin 2ax+\frac{x}{4a^2}\cos 2ax+C$

$\int x^n\cos axdx=\frac{x^n\sin ax}{a}-\frac{n}{a}\int x^{n-1}\sin axdx$

$\int \frac{\cos ax}{x}dx=\ln |ax|+\sum _{k=1}^{\mathrm{\infty }}(-1{)}^k\frac{(ax{)}^{2k}}{2k\cdot (2k)!}+C$

$\int \frac{\cos ax}{x^n}dx=-\frac{\cos ax}{(n-1)x^{n-1}}-\frac{a}{n-1}\int \frac{\sin ax}{x^{n-1}}dx\text{(for }n\ne 1\text{)}$

$\int \frac{dx}{\cos ax}=\frac{1}{a}\ln |\tan (\frac{ax}{2}+\frac{\pi }{4})|+C$

$\int \frac{dx}{{\cos }^{n}ax}=\frac{\sin ax}{a(n-1){\cos }^{n-1}ax}+\frac{n-2}{n-1}\int \frac{dx}{{\cos }^{n-2}ax}\text{(for }n>1\text{)}$

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

$\int \frac{dx}{1-\cos ax}=-\frac{1}{a}\cot \frac{ax}{2}+C$

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

$\int \frac{xdx}{1-\cos ax}=-\frac{x}{a}\cot \frac{ax}{2}+\frac{2}{a^2}\ln |\sin \frac{ax}{2}|+C$

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

$\int \frac{\cos axdx}{1-\cos ax}=-x-\frac{1}{a}\cot \frac{ax}{2}+C$

$\int \cos a_{1}x\cos a_{2}xdx=\frac{\sin (a_1-a_2)x}{2(a_1-a_2)}+\frac{\sin (a_1+a_2)x}{2(a_1+a_2)}+C\text{(for }|a_1|\ne |a_2|\text{)}$