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Manipal MET2010MathematicsIndefinite Integration

Evaluate 1 (x+1) x^2-1 d x

Options

  1. Ax+1 x-1 +c
  2. Bx-1 x+1 +c
  3. C1 x+1 +c
  4. DNone of these

Correct answer

B. x-1 x+1 +c

Step-by-step solution

Let I= 1 (x+1) x^2-1 d x Put, x+1= 1 t d x=- 1 t^2 d t , then I= 1 1 t ( 1 t -1 )^2-1 ( -1 t^2 ) d t I=- d t 1-2 t =- (1-2 t)^ -1 / 2 d t=- (1-2 t)^ 1 / 2 (-2) ( 1 2 ) +c I= 1-2 t +c I= 1- 2 x+1 +c I= x-1 x+1 +c

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