Integračné vzorce

1. \(\displaystyle\int k\,dx=kx+C\), kde \(k\in\mathbb R\).
2. \(\displaystyle\int x^a\,dx=\frac{x^{a+1}}{a+1}+C\), kde \(a\neq-1\).
3. \(\displaystyle\int\frac1x\,dx=\ln|x|+C\), kde \(x\neq0\).
4. \(\displaystyle\int e^x\,dx=e^x+C\).
5. \(\displaystyle\int a^x\,dx=\frac{a^x}{\ln a}+C\), kde \(a>0\) a \(a\neq1\).
6. \(\displaystyle\int\sin x\,dx=-\cos x+C\).
7. \(\displaystyle\int\cos x\,dx=\sin x+C\).
8. \(\displaystyle\int\frac1{\cos^2x}\,dx=\tan x+C\).
9. \(\displaystyle\int\frac1{\sin^2x}\,dx=-\cot x+C\).
10. \(\displaystyle\int\frac1{1+x^2}\,dx=\arctan x+C\).
11. \(\displaystyle\int\frac1{\sqrt{1-x^2}}\,dx=\arcsin x+C\), kde \(-1<x<1\).
12. \(\displaystyle\int\frac{f'(x)}{f(x)}\,dx=\ln|f(x)|+C\), kde \(f(x)\neq0\).