1. $\int kdx=kx+C　(k是常数)$

2. $\int x^{\mu } dx=\frac{x^{\mu+1} }{\mu+1} +C　(\mu\ne -1)$

3. $\int \frac{dx}{x} =\ln_{}{\left |x \right | } +C$

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

5. $\int \frac{1}{\sqrt{1-x^{2} } } dx=\arcsin x+C$

6. $\int \cos xdx=\sin x+C$

7. $\int \sin xdx=-\cos x+C$

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

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

10. $\int \sec x\tan xdx=\sec x+C$

11. $\int \csc x\cot xdx=- \csc x+C$

12. $\int e^{x} dx=e^{x}+C$

13. $\int a^{x} dx=\frac{a^{x}}{\ln_{}{a} } +C$

14. $\int \tan xdx=-\ln_{}{\left |\cos x \right | } +C$

15. $\int \cot xdx=\ln_{}{\left |\sin x \right | } +C$

16. $\int \sec xdx=\ln_{}{\left |\sec x+\tan x \right | } +C$

17. $\int \csc xdx=\ln_{}{\left |\csc x-\cot x \right | } +C$

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

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

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

21. $\int \frac{1}{\sqrt{a^{2}-x^{2} } } dx=\arcsin \frac{x}{a} +C$

22. $\int \frac{1}{\sqrt{x^{2}\pm a^{2} } } dx=\ln_{}{\left | x+\sqrt{x^{2}\pm a^{2} } \right | } +C$

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