$\int_{}^{}{\mathbf{\text{dx}} = x\ \ \ \ \ \ \ \int_{}^{}{\mathbf{x}^{\mathbf{n}}\mathbf{\text{dx}} = \frac{1}{n + 1}x^{n + 1}\text{\ \ \ \ \ \ }\int_{}^{}\mathbf{\text{xdx}} = \frac{1}{2}x^{2}\text{\ \ \ \ \ \ \ }\int_{}^{}{\frac{\mathbf{1}}{\mathbf{x}}\mathbf{\text{dx}} = \ln\left| x \right|}}}$

$\int_{}^{}{\mathbf{a}^{\mathbf{x}}\mathbf{\text{dx}} = \frac{a^{x}}{\text{lna}}\text{\ \ \ \ \ \ \ }\int_{}^{}{\mathbf{e}^{\mathbf{x}}\mathbf{\text{dx}} = e^{x}\text{\ \ \ \ \ }\int_{}^{}{\mathbf{\text{sixdx}} = - cosx\ \ \ \ \int_{}^{}{\mathbf{\text{cosxdx}} = sinx}}}}$

∫tgxdx = −ln|cocx| ∫ctgxdx = ln|sinx| $\int_{}^{}\frac{\text{dx}}{\cos^{2}x}$=tgx. $\int_{}^{}\frac{\mathbf{\text{dx}}}{\mathbf{\sin}^{\mathbf{2}}\mathbf{x}}$=-ctgx. $\int_{}^{}\frac{\mathbf{\text{dx}}}{\mathbf{x}^{\mathbf{2}}\mathbf{+}\mathbf{a}^{\mathbf{2}}}$=$\frac{\mathbf{1}}{\mathbf{a}}$arctg$\frac{x}{a}$. $\int_{}^{}\frac{\mathbf{\text{dx}}}{\mathbf{x}^{\mathbf{2}}\mathbf{-}\mathbf{a}^{\mathbf{2}}} = \frac{1}{2a}$ln$|\frac{x - a}{x + a}$

$\int_{}^{}\frac{\mathbf{\text{dx}}}{\sqrt{\mathbf{a}^{\mathbf{2}}\mathbf{-}\mathbf{x}^{\mathbf{2}}}}$= arcsin$\frac{x}{a}$.$\mathbf{\ }\int_{}^{}\frac{\mathbf{\text{dx}}}{\sqrt{\mathbf{x}^{\mathbf{2}}\mathbf{+}\mathbf{a}^{\mathbf{2}}}}$=ln|x$\sqrt{x^{2} + a}$|.

$\int_{}^{}{\mathbf{\text{dx}} = x\text{\ \ \ \ \ \ \ }\int_{}^{}{\mathbf{x}^{\mathbf{n}}\mathbf{\text{dx}} = \frac{1}{n + 1}x^{n + 1}\text{\ \ \ \ \ \ }\int_{}^{}\mathbf{\text{xdx}} = \frac{1}{2}x^{2}\text{\ \ \ \ \ \ \ }\int_{}^{}{\frac{\mathbf{1}}{\mathbf{x}}\mathbf{\text{dx}} = \ln\left| x \right|}}}$

$\int_{}^{}{\mathbf{a}^{\mathbf{x}}\mathbf{\text{dx}} = \frac{a^{x}}{\text{lna}}\text{\ \ \ \ \ \ \ }\int_{}^{}{\mathbf{e}^{\mathbf{x}}\mathbf{\text{dx}} = e^{x}\text{\ \ \ \ \ }\int_{}^{}{\mathbf{\text{sixdx}} = - \text{cosx}\text{\ \ \ \ }\int_{}^{}{\mathbf{\text{cosxdx}} = \text{sinx}}}}}$

∫tgxdx = −ln|cocx| ∫ctgxdx = ln|sinx| $\int_{}^{}\frac{\text{dx}}{\cos^{2}x}$=tgx. $\int_{}^{}\frac{\mathbf{\text{dx}}}{\mathbf{\sin}^{\mathbf{2}}\mathbf{x}}$=-ctgx. $\int_{}^{}\frac{\mathbf{\text{dx}}}{\mathbf{x}^{\mathbf{2}}\mathbf{+}\mathbf{a}^{\mathbf{2}}}$=$\frac{\mathbf{1}}{\mathbf{a}}$arctg$\frac{x}{a}$. $\int_{}^{}\frac{\mathbf{\text{dx}}}{\mathbf{x}^{\mathbf{2}}\mathbf{-}\mathbf{a}^{\mathbf{2}}} = \frac{1}{2a}$ln$|\frac{x - a}{x + a}$

$\int_{}^{}\frac{\mathbf{\text{dx}}}{\sqrt{\mathbf{a}^{\mathbf{2}}\mathbf{-}\mathbf{x}^{\mathbf{2}}}}$= arcsin$\frac{x}{a}$.$\mathbf{\ }\int_{}^{}\frac{\mathbf{\text{dx}}}{\sqrt{\mathbf{x}^{\mathbf{2}}\mathbf{+}\mathbf{a}^{\mathbf{2}}}}$=ln|x$\sqrt{x^{2} + a}$|.