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MHT CET202014 Oct 2020Evening ShiftMathematicsIndefinite IntegrationActual

[ (1+ x)-x ( x 2 ) ] d x=

Options

  1. Ax |x|+c
  2. Bx |1+ x|+c
  3. Cx | x 2 |+c
  4. Dx |1+ x|+c

Correct answer

D. x |1+ x|+c

Step-by-step solution

aligned I &= [ (1+ x)-x ( x 2 ) ] d x I &= (1+ x) 1 d x- x x 2 d x &=x (1+ x)- (- x)(x) 1+ x d x- x x 2 aligned =x (1+ x)+ x (2 x 2 x 2 ) 2 ² x 2 d x- x x 2 d x=x (1+ x)+ x x 2 d x- x x 2 d x=x (1+ x)+c

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