Evaluate

Asked by Rahulsinha1993 | 7th Sep, 2010, 08:53: PM

Expert Answer:

x2/(x2 - 4x + 3) = x2/((x - 3)(x - 1))
Using partial fractions,
x2/((x - 3)(x - 1)) = A/(x - 3) + B/(x - 1)
x2 = A(x - 1) + B(x - 3)
Put x = 1, and we find B = -1/2
and x = 3 and we find A = 9/2
Hence,
x2/((x - 3)(x - 1)) = 9/2(x - 3) - 1/2(x - 1)
Now ∫x2 dx/((x - 3)(x - 1)) = ∫(9/2(x - 3) - 1/2(x - 1)) dx
= (9/2) ln(x - 3) - (1/2) ln(x - 1) + C
= ln [(x - 3)9/(x - 1)]1/2 + C
Regards,
Team,
TopperLearning.
 

Answered by  | 7th Sep, 2010, 09:22: PM

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