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a
=−12log|x−1|−16log|x+2|+13log|x−3|+C
b
=−13log|x−1|−16log|x+2|+12log|x−3|+C
c
=−16log|x−1|−13log|x+2|+12log|x−3|+C
d
None of these
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Correct option is C
Since all the factors in the denominator are linear, we have ∫2x−1(x−1)(x+2)(x−3)dxformula: If f(x)g(x)=A1x-a1+A2x-a2+A3x-a3+.......Anx-an where g(x)=x-a1x-a2x-a3....x-anthen A1=f(a1)a1-a2a1-a3...a1-an , A1=f(a2)a2-a1a2-a3...a2-an, ........ An=f(an)an-a1an-a2...an-an-1=∫1(x−1)(3)(−2)+−5(−3)(x+2)(−5)+5(2)(5)(x−3)dx=−16log|x−1|−13log|x+2|+12log|x−3|+CSimilar Questions
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