Q. 18

Find :<span

Answer :




let 2x = t


dt = 2dx




The above equation of the form





OR


By Partial Fraction:



Cancelling the denominator



Putting x = - 2


( - 2)2 + ( - 2) + 1 = A(( - 2)2 + 1) + 0


= 4 - 2 + 1 = 5A



Putting x = 0


We get



Putting x = 1




Hence our equation becomes





I1 =


=


I2


Let t = x2 + 1



dt = 2xdx


Substituting,





I3




Hence,


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