Ex 7.5, 4 - Integrate x / (x - 1) (x - 2) (x - 3) - Ex 7.5

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex 7.5, 4 π‘₯/(π‘₯ βˆ’ 1)(π‘₯ βˆ’ 2)(π‘₯ βˆ’ 3) . We can write the integrand as π‘₯/((π‘₯ βˆ’ 1) (π‘₯ βˆ’ 2) (π‘₯ βˆ’ 3) ) = 𝐴/((π‘₯ βˆ’ 1) ) + 𝐡/((π‘₯ βˆ’ 2) ) + 𝐢/((π‘₯ βˆ’ 3) ) = (𝐴(π‘₯ βˆ’ 2)(π‘₯ βˆ’ 3) + 𝐡(π‘₯ βˆ’ 1)(π‘₯ βˆ’ 3) + 𝐢(π‘₯ βˆ’1)(π‘₯ βˆ’ 2))/((π‘₯ βˆ’ 1) (π‘₯ βˆ’ 2) (π‘₯ βˆ’ 3) ) By cancelling denominator π‘₯ = 𝐴(π‘₯βˆ’2)(π‘₯βˆ’3)+𝐡(π‘₯βˆ’1)(π‘₯βˆ’3)+𝐢(π‘₯βˆ’1)(π‘₯βˆ’2) Putting π‘₯=1, in (1) 1 = 𝐴(1βˆ’2)(1βˆ’3)+𝐡(1βˆ’1)(1βˆ’3)+𝐢(1βˆ’1)(1βˆ’2) 1 = 𝐴(βˆ’1)(βˆ’2)+𝐡×0+𝐢×0 1 = 2𝐴

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