# Table of Integrals

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