Таблица интегралов

1. $\int 0dx=C$
2. $\int 1dx=x+C$
3. $\int x^{n}dx=\frac{x^{n+1}}{n+1}+C$
4. $\int x^{-n}dx=\frac{x^{-n+1}}{-n+1}+C$
5. $\int x^{\alpha }dx=\frac{x^{\alpha +1}}{\alpha +1}+C$
6. $\int \frac{1}{x}dx=\ln |x|+c$
7. $\int a^{x}dx=\frac{a^x}{\ln a}+C$
8. $\int e^{x}dx=e^x+c$
9. $\int \sin xdx=-\cos x+C$
10. $\int \cos xdx=\sin x+C$
11. $\int \frac{dx}{{\cos }^{2}x}=\tan x+C$
12. $\int \frac{dx}{{\sin }^{2}x}=-\cot x+C$
13. $\int \frac{dx}{\sqrt{1-x^2}}=\arcsin x+C$
14. $\int \frac{dx}{1+x^2}=\arctan x+C$

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