| NR | Całka |
|---|---|
| 1. | \(\displaystyle\int 0\,dx=C\) |
| 2. | \(\displaystyle \int a\,dx= ax+C\,\,\,\,\,\,\,\,a\in \mathbb{R}\setminus \left \{ 0 \right \}\) |
| 3. | \(\displaystyle \int x^{n}\,dx=\frac{x^{n+1}}{n+1}+C\,\,\,\,\,\,\,\, n\neq -1\) |
| 4. | \(\displaystyle \int \frac{1}{x}dx=\ln|x|+C\) |
| 5. | \(\displaystyle \int a^x\,dx=\frac{a^x}{\ln a}+C\) |
| 6. | \(\displaystyle \int e^x=e^x+C\) |
| 7. | \(\displaystyle \int\sin x\, dx=-\cos x +C\) |
| 8. | \(\displaystyle \int\cos x\,dx=\sin x +C\) |
| 9. | \(\displaystyle \int\text{tg} \,x\,dx=- \ln|\cos x| +C\) |
| 10. | \(\displaystyle \int\text{ctg} \,x\,dx= \ln|\sin x| +C\) |
| 11. | \(\displaystyle \int \frac {dx}{\sin^2 x}=-\text{ctg}\, x+C\) |
| 12. | \(\displaystyle \int \frac {dx}{\cos^2 x}=\text{tg} \,x +C\) |
| 13. | \(\displaystyle \int \frac {dx}{\sqrt{1-x^2}} =\text{arc} \sin x+C\) |
| 14. | \(\displaystyle \int \frac {dx}{{1+x^2}}=\text{arc}\, \text{tg} x+C\) |