Таблица интегралов

1. $\int dx=x+C$

2. $\int x^{\alpha}dx=\frac{x^{\alpha+1}}{\alpha+1}+C$

3. $\int \frac{dx}{x}=\ln |x|+C$

4. $\int a^x dx=\frac{a^x}{\ln a}+C$

5. $\int e^x dx=e^x+C$

6. $\int \sin x dx=-\cos x+C$

7. $\int \cos x dx=\sin x+C$

8. $\int \frac{dx}{\cos^2 x}=tg x+C$

9. $\int \frac{dx}{sin^2 x}=-ctg x+C$

10. $\int \frac{dx}{\sqrt{a^2-x^2}}=\arcsin\frac{x}{a}+C$

11. $\int \frac{dx}{\sqrt{x^2 \pm a^2}}=\ln\left|x+\sqrt{x^2\pm a^2}\right|+C$

12. $\int \frac{dx}{x^2+a^2}=\frac{1}{a}arctg\frac{x}{a}+C$

13. $\int \frac{dx}{x^2 -a^2}=\frac{1}{2a}\ln\left|\frac{x-a}{x+a}\right|+C$

14. $\int sh x dx = ch x+C$

15. $\int ch x dx = sh x+C$

16. $\int \frac{dx}{ch^2 x} = th x+C$

17. $\int \frac{dx}{sh^2 x} = -cth x+C$