﻿﻿ Math.by - Таблица неопределенных интегралов

### Неопределенные интегралы

 1 $\int x^n dx = \frac{x^{n+1}}{n+1} + C, \quad n \in Z, n \ne-1, C = const$ 2 $\int \frac{dx}{x} = \ln{|x|} + C, \quad x \ne 0, C = const$ 3 $\int \sqrt{x} dx = \frac{2}{3} x^{\frac{3}{2}} + C, \quad C = const$ 4 $\int \frac{dx}{\sqrt{x}} = 2 \sqrt{x} + C, \quad C = const$ 5 $\int e^{x} dx = e^{x} + C, \quad C = const$ 6 $\int a^{x} dx = \frac{a^{x}}{\ln{a}} + C, \quad a > 0 , C = const$ 7 $\int \ln{x} dx = x \ln{x} - x + C, \quad C = const$ 8 $\int \log_{a}{x} dx = \frac{1}{\ln {a}} (x \ln{x} - x) + C, \quad a > 0 , C = const$ 9 $\int \sin{x} dx = -\cos{x} + C, \quad C = const$ 10 $\int \cos{x} dx = \sin{x} + C, \quad C = const$ 11 $\int \tan{x} dx = - \ln{|\cos{x}|} + C, \quad C = const$ 12 $\int \cot{x} dx = \ln{|\sin{x}|} + C, \quad C = const$ 13 $\int \arcsin{x} dx = x \arcsin{x} + \sqrt{1-x^2} + C, \quad C = const$ 14 $\int \arccos{x} dx = x \arccos{x} - \sqrt{1-x^2} + C, \quad C = const$ 15 $\int \arctan{x} dx = x \arctan{x} - \frac{1}{2} \ln(1 + x^2) + C, \quad C = const$

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