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MHT CET20244 May 2024Evening ShiftMathematicsIndefinite IntegrationActual

(x^2+1 ) (x+1)^2 d x=

Options

  1. Ax-2 |(x+1)|- 1 x+1 +c , where c is a constant of integration.
  2. Bx-2 |(x+1)|- 2 x+1 + c , where c is a constant of integration.
  3. Cx- |(x+1)|- 2 x+1 +c , where c is a constant of integration.
  4. Dx- |(x+1)|- x x+1 +c , where c is a constant of integration.

Correct answer

B. x-2 |(x+1)|- 2 x+1 + c , where c is a constant of integration.

Step-by-step solution

Let aligned I & = (x^2+1 ) (x+1)^2 ~d x & = (x^2+2 x+1-2 x ) (x+1)^2 ~d x & = (x+1)^2 (x+1)^2 ~d x- 2 x (x+1)^2 ~d x & = 1 ~d x- 2 x (x+1)^2 ~d x & = 1 ~d x- 2 x+2-2 (x+1)^2 ~d x & =x-2 (x+1) (x+1)^2 +2 1 (x+1)^2 ~d x & =x-2 1 x+1 ~d x+2 1 (x+1)^2 ~d x aligned =x-2 (x+1)- 2 (x+1) +c

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