Integral
The integral of the product of a constant and a function is equal to be product of the constant and the integral of the function
The integral or sum of aur differentiation of a finite number of function is equal to sum or difference of integrals
Integration of Trigonometric Functions Formulas
- ∫sin x dx = -cos x
- ∫cos x dx = sin x
- ∫tan x dx = ln|sec x|
- ∫sec x dx = ln|tan x + sec x|
- ∫cosec x dx = ln|cosec x – cot x| + C = ln|tan(x/2)|
- ∫cot x dx = ln[sin x|
- ∫sec2x dx = tan x
- ∫cosec2x dx = -cot x
- ∫sec x tan x dx = sec x
- ∫cosec x cot x dx = -cosec x
- ∫sin ax dx = -(cos ax/a)
- ∫cos ax dx = (sin ax/a)
Method of integration
There are variable method of integration by which we can reduce the given integral to one of the known standard integral.
Integration by substitution
A change in the variable of integration often reduce an integral to one of fundamental integrals
Some important formulae based on the above form
![](https://1.bp.blogspot.com/-vu2UnfQD9iA/XxPtIQO4nzI/AAAAAAAAAUY/nwclL34_g3onMzvmmy9eKDV7FHQrC0gygCLcBGAsYHQ/s640/CV_502872735285405.jpg)
![](https://1.bp.blogspot.com/--y0U9AMdb_0/XxPtISGkPFI/AAAAAAAAAUc/KlRP--7oTqcdXDeMsUz4d924WN_LtAvbQCLcBGAsYHQ/s640/CV_502874798014519.jpg)
If the integrated consists of the product of a constant power power of a function f(x) and the derivative f'(x) of f(x), to obtain the integral will increase the index by unity and then divide by increased index. This is known power formula.
![](https://1.bp.blogspot.com/-H8nx_6RuTmU/XxPtJZlPdhI/AAAAAAAAAUo/MDpE95ff5Oo12zCOhyxHvNTpRxlFzD4CQCLcBGAsYHQ/s640/CV_502877264635091.jpg)
Integral of the product off to function
Integration by part
Formula base upon about method
![](https://1.bp.blogspot.com/-hVsBh_KHhGc/XxPtJc7dCjI/AAAAAAAAAUk/ePhQ9nyQKMosT9QjM7Strfh8L92BczO8QCLcBGAsYHQ/s640/CV_502879870514725.jpg)
The following is a summary of some of the integrals derived so far by using the three method of integration
![](https://1.bp.blogspot.com/-K6f5a487PDE/XxPtJtQ2czI/AAAAAAAAAUs/jNbBoAqkDKAHWCD20GcID9W1P1-BMczSACLcBGAsYHQ/s640/CV_502884515102952.jpg)
![](https://1.bp.blogspot.com/-559Q_245ZeA/XxPtK1zesJI/AAAAAAAAAUw/RTaDI9W9XI8ugVQYxXuQpVmulsUsUH3LwCLcBGAsYHQ/s640/CV_502886160620087.jpg)