Integration formulae

\[\int{I.II.dx} =I.\int{IIdx-\int{[\int{IIdx].dI/dx .dx}}}\]

\[\int{}\]e^x[f(x) + f'(x) ]dx=e^xf(x) 

1. \[\int{x}^ndx=\frac{x^n+1}{n+1 } if n\neq -1\]
2. \[\int{dx/x} =logx\]
3. \[\int{sinxdx}=-cosx\]
4. \[\int{cosxdx}=sinx\]
5. \[\int{sec^2xdx}=tanx\]
6. \[\int{cosec^2xdx}=-cotx\]
7. \[\int{secxtanxdx}=secx\]
8. \[\int{cosecxcotxdx}=-cosecx\]
9. \[\int{tanxdx}=logsecx\]
10. \[\int{cotxdx}=-logcosecx=logsinx\]
11. \[\int{secxdx}=log{tan(x/2 +π/4) }=log(secx+tanx) \]
12. \[\int{cosecxdx}=log(tan(x/2 ) )=log(cosecx-cotx) \]
13. \[\int{e^x}dx=e^x\]
14. \[\int{a^x}dx=a^x/loga\]
15. \[\int{dx/\sqrt{a^2-x^2}}=sin^{-1}(x/a)\]
16. \[\int{dx/\sqrt{x^2-a^2}}=log(x+\sqrt{x^2-a^2}) \]
17. \[\int{dx/\sqrt{x^2+a^2}}=log(x+\sqrt{x^2+a^2}) \]
18. \[\int{dx/x^2+a^2} =1/a ×tan^{-1}(x/a)\]
19. \[\int{dx/x^2-a^2} =1/2a ×log\frac{x-a}{x+a}\]
20. \[\int{dx/a^2-x^2} =1/2a ×log\frac{a+x}{a-x}\]
21. \[\int{sinhxdx}=coshx\]
22. \[\int{coshxdx}=sinhx\]
23. \[\int{tanhxdx}=log(coshx) \]
24. \[\int{sechxdx}=sin^{-1}(tanhx)\]