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MHT CET20226 Aug 2022Evening ShiftMathematicsIndefinite IntegrationActual

3 x-2 (x+1)(x-2)^2 d x= (where C is a constant of integration.)

Options

  1. A-5 9 (x+1)+ 5 9 (x-2)- 4 3 1 (x-2) +C
  2. B1 9 (x+1)+ 5 9 (x-2)- 4 3 1 (x-2) +C
  3. C-5 9 (x+1)+ 5 9 (x-2)- 4 3 1 x-2 +C
  4. D-5 9 (x+1)+ 1 9 (x-2)+ 1 x-2 +C

Correct answer

A. -5 9 (x+1)+ 5 9 (x-2)- 4 3 1 (x-2) +C

Step-by-step solution

3 x-2 (x+1)(x-2)^2 d x= -5 9(x+1) + 5 9(x-2) + 4 3(x-2)^2 d x [Using partial fraction] =- 5 9 |x+1|+ 5 9 |x-2|- 4 3(x-2) +C

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