$$\int_{}^{}{\frac{1}{\sin^{n}x} = \ - \frac{1}{n - 1}*\frac{1}{\sin^{n - 2}x}\text{ctg}x + \frac{n - 2}{n - 1}\int_{}^{}{\frac{1}{\sin^{n - 2}x}\text{dx}}}$$

$$\int_{}^{}{\frac{1}{\cos^{n}x} = \ \frac{1}{n - 1}*\frac{1}{\cos^{n - 2}x}tgx + \frac{n - 2}{n - 1}\int_{}^{}{\frac{1}{\cos^{n - 2}x}\text{dx}}}$$

$$\int_{}^{}{\sin^{n}x = \ - \frac{1}{n}\sin^{n - 1}xcosx + \frac{n - 1}{n}\int_{}^{}{\sin^{n - 2}\text{xdx}}}$$

$$\int_{}^{}{\cos^{n}x = \ \frac{1}{n}\cos^{n - 1}xsinx + \frac{n - 1}{n}\int_{}^{}{\cos^{n - 2}\text{xdx}}}$$

$$\int_{}^{}{\text{ctg}^{n}x = \ - \frac{1}{n - 1}\text{ctg}^{n - 1} - \int_{}^{}{\text{ctg}^{n - 2}\text{xdx}}}$$

$$\int_{}^{}{\text{tg}^{n}x = \ \frac{1}{n - 1}\text{tg}^{n - 1} - \int_{}^{}{\text{tg}^{n - 2}\text{xdx}}}$$

$$ax^{2} + bx + c = {(ax + \frac{b}{2})}^{2} - \left( \frac{b}{2} \right)^{2} + d$$