Integrate the (rational) function in

 

SOLUTION:

 …….(i)

 

 

Comparing coefficients of  on both sides A + B = 1 …..(ii)

Comparing constants 2A + B = 0 …..(iii)

Solving eq. (ii) and (iii), we get A =  and B = 2

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

 

=−log|x+1|+2log|x+2|+c=−log|x+1|+2log|x+2|+c

= 

=