Indefinite Integrals


   
 
Some Special Types of Integrals (Contd…)
Example:
 
Evaluate the integral
 
Suggested answer:
 
Referring to the above procedure (ii), we have
 
 
 
Comparing the coefficients of x and
 
4A = 1 B = 1
 
B = 1
 
 
 
 
 
 
Put (2x2 + 3) = t
 
 
 
 
 
 
 
 
 
 
Substituting I1 and I2 from (2) and (3) respectively in (1) we have
 
 
Integral of the form
 
Method:
 
Taking 1 as the second function and integrating by parts, we get
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Integral of the form
 
Method:
 
We make the substitution
 
 
 
(1+t2)dx 2dt
 
 
 
 
Similarly,
 
 
 
By making the above substitutions the integrals will be reduced to the form  which can be integrated by method of completing squares.
 
Example:
 
 
Suggested answer:
 
 
 
 
 
 
 
 
 
 
 
 
dt = dZ
 
 
 
 
 
 
  
     
   
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