Q. 73.6( 60 Votes )

Integrate the rat

Answer :

Let

x = (Ax + B)(x -1) + C (x2 + 1)


x = Ax2 – Ax + Bx – B + Cx2 + C


Equating the coefficients of x2, x and constant term, we get,


A + C = 0


-A + B = 0


-B + c = 0


On solving these equation, we get,


A = , B = and C =


Thus,





Now, let us consider, ,


Let (x2 + 1) = t


2xdx = dt


Thus,



Therefore,




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