Derived Substitution:

At times it is useful to write the integral as a sum of 2 related integrals which can be evaluated by making appropriate substitutions.

Examples of such type of integrals are:

A. Algebraic Twins

B. Trigonometric twins

Method of evaluating these integral are explained by mean of following  examples:

 Example: Evaluate .

Solution:        

                        For I₁, we write  x -1/x = t  => 

                        For  I₂ ,  we write  

                        Combining the 2 integrals, we get

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