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NDA2021MathematicsIndefinite IntegrationActual

What is d x x+ x equal to ?

Options

  1. A( x)+ | x+ x|+c
  2. B( x)- | x+ x|+c
  3. Cx x- | x- x|+c
  4. D| x+ x|- | x|+c

Correct answer

D. | x+ x|- | x|+c

Step-by-step solution

aligned I & = d x x+ x = ( x- x) d x ( ^2 x- ^2 x ) & = x d x- x d x & =l n|( x+ x)|-(- nn | x|)+C & =l n| x+ x|-l n | x|⁻¹+C & =l n| x+ x|-l n | x|+C aligned

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