Integrate the (rational) function in

 

SOLUTION:

= 

= 

=  (Dividing numerator by denominator)

 

=  …….(i)

Now 

=  …….(ii)

 

 

Comparing coefficients of  on both sides –2A + B =  …..(iii)

Comparing constants A = 1 …….(iv)

Solving eq. (ii) and (iii), we get A =  and B = 

Putting these values of A and B in eq. (ii),

 

= 

= 

Putting this value in eq. (i),

=