Основные интегралы — различия между версиями

Версия 15:42, 21 марта 2009

<math>~\int\!0\, dx = C</math>

<math>~\int\!\,dx = x +C</math>

<math>~\int\!\sqrt{x}\,dx = {2 \over 3} x\sqrt{x} +C</math>

<math>~\int\!x^n\,dx = \frac{x^{n+1}}{n+1} + C,\,n \ne -1</math>

<math>\int {dx\over x}\, = \ln \left|x \right| + C</math>

<math>\int {dx\over \sqrt{x}}\, = 2\sqrt{x} + C</math>

<math>\int {dx\over x^2}\, = {-1 \over x} + C</math>

<math>\int\!e^x\,dx = e^x + C</math>

<math>\int\!a^x\,dx = \frac{a^x}{\ln{a}} + C</math>

<math>\int\!\sin{x}\, dx = -\cos{x} + C</math>

<math>\int\!\cos{x}\, dx = \sin{x} + C</math>

<math>\int\!{dx \over \cos^2 x} = \operatorname{tg}\,x + C</math>

<math>\int\!{dx \over \sin^2 x} = - \operatorname{ctg}\,x + C</math>

<math>\int\!{dx \over {1+x^2}} = \operatorname{arctg}\,x + C</math>

<math>\int\!{dx \over \sqrt{1-x^2}} = \arcsin {x} + C</math>

<math>\int\!{-dx \over \sqrt{1-x^2}} = \arccos {x} + C</math>

<math>\int \operatorname{sh}\,x \, dx = \operatorname{ch}\,x + C</math>

<math>\int \operatorname{ch}\,x \, dx = \operatorname{sh}\,x + C</math>

<math>\int\!{dx \over \operatorname{ch}^2 x} = \operatorname{th}\,x + C</math>

<math>\int\!{dx \over \operatorname{sh}^2 x} = - \operatorname{cth}\,x + C</math>