Indefinite integral calculates the original function (the result is a formula), definite integral calculates the specific value (the loan is a specific number), indefinite integral is the inverse operation of differential, and definite integral is an accumulated fraction on the basis of indefinite integral, replacing numerical value with subtraction integral. Now, there are many complete activities on the Internet. Like all kinds of emails, qq, etc. In calculus, integration is the inverse operation of differentiation, that is, knowing the derivative function of a function and finding the original function in reverse. In application, the function of integration is not only this, but also widely used in summation, that is, to find the area of curved triangle. This ingenious solution is determined by the special properties of integral. The indefinite integral of a function (also called the original function) refers to another family of functions. The derivative function of this family of functions distributes the differential operator to the previous function in the first bracket, and finally both sides are multiplied by R 4.

=f''''+( 1/r)f'''-(4/r^2)f''

+[(- 1/r^2)f'+( 1/r)f'']'+( 1/r)[(- 1/r^2)f'+( 1/r)f'']-(4/r^3)f'

-4[( 1/r^2)f'-(2/r^3)f]'-(4/r)[( 1/r^2)f'-(2/r^3)f]+( 16/r^4)f

=f''''+( 1/r)f'''-(4/r^2)f''

+[(2/r^3)f'-( 1/r^2)f''-( 1/r^2)f''+( 1/r)f''']+( 1/r)[(- 1/r^2)f'+( 1/r)f'']-(4/r^3)f'

-4[(-2/r^3)f'+( 1/r^2)f''+(6/r^4)f-(2/r^3)f']-(4/r)[( 1/r^2)f'-(2/r^3)f]+( 16/r^4)f

Multiply both sides by r 4 and merge the items.