mathdic-积分表

小时候，暑假很长，窗外永远郁郁葱葱

基本积分表

1. $\int0\mathrm{d}x =C$.
2. $\int1\mathrm{d}x =\int{\mathrm{d}x }=x+C$.
3. $\int{x^{\alpha}}\mathrm{d}x =\frac{x^{\alpha+1}}{\alpha+1}+C$$\ (\alpha\ne-1,x>0)$.
4. $\int\frac{1}{x}\mathrm{d}x =ln|x|+C$ $\ (x\ne0)$.
5. $\int {e^x}\mathrm{d}x =e^x+C$.
6. $\int {a^x}\mathrm{d}x ={a^x}$.
7. $\int cos\ {ax}\mathrm{d}x =\frac{1}{a}sin\ ax+C$$\ (a\ne 0)$.
8. $\int sin\ ax\mathrm{d}x =-\frac{1}{a}cos\ ax+C$$\ (a\ne 0)$.
9. $\int sec^2x\mathrm{d}x =tan\ x+C$.
10. $\int csc^2x\mathrm{d}x =-cot\ x+C$.
11. $\int sec\ x\cdot tan\ x\mathrm{d}x = sec\ x+C$.
12. $\int csc\ x\cdot cot\ x\mathrm{d}x = - csc\ x+C$.
13. $\int \frac{\mathrm{d}x}{\sqrt{1-x^2}} = arcsin\ x+C=-arccos\ x+C_1$.
14. $\int \frac{\mathrm{d}x}{1+x^2} = arctan\ x+C=-arccot\ x+C_1$.