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Dear all, You might all be afraid of integration though it is quite fascinating topic... Well, here we bring up few important concepts in integration, by which you can make your preparation interesting...!!

Indefinite Integrals

A function is called a primitive (or) an anti derivative of a function f(x) of

Here f(x) = integrand

Algorithm to solve integrals of form:

, and
where

Step 1: Find m,n

Step 2:

• If m is odd i.e. power or index of sin x is odd, put cos x = t and reduced the integrand in terms of it
• If n is odd then put sin x = t and reduce the integrand
• If both are odd you can use any of above two methods

To Evaluate integrals of form

• where and m+n is negative even integer then put tan x = t.
• To evaluate integrals of form where m,n are positive even integers then.

  Let Z = cos x + i sin x

  
  
  
  
  

Some important standard integrals :

Integrals of form

to evaluate this type of integrals

Depending on integral then find

Now integrate both sides of expression to get required integral.

Integration by parts :

Very IMP Note:

Choose first function as the function which come first in word “ILATE”

I – Inverse trigonometric

L – logarithmic functions

A – algebraic functions

T for Trigonometric functions

E for exponential functions

Integrals of the form

Note:

Some very important integrals:

Reduction formulae:

Your comments and questions are warmly welcomed....