Integration is the inverse process of differentiation. In the differential calculus, you are given a function and you have to find the derivative or differential of this function, but in the integral calculus, you are to find a function whose differential is given. Thus, integration is a process which is the inverse of differentiation.

Indefinite Integrals

Indefinite integrals are also called general integrals. C is called constant of integration. All these integrals differ by a constant. From the geometric point of view, an indefinite integral is collection of family of curves, each of which is obtained by translating one of the curves parallel to itself upwards or downwards along the y-axis.

Some Standard Integrals

 

Integration By Partial Fractions

A rational function can be integrated by expressing it as the sum of partial fractions.

Integration By Substitution

A change in the variable of integration often reduces an integral to one of the fundamental integrals. The method in which you change the variable to some other variable is called the method of substitution. When the integrand involves some trigonometric functions, you can some well known identities to find the integrals. 

 

Integrals of Special Functions