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MHT CET202616 April 2026Morning ShiftMathematicsIndefinite IntegrationActual

^4 x ,dx is equal to

Options

  1. A^3 x 3 - x + x + c
  2. B^3 x 3 + x + x + c
  3. C- ^3 x 3 + x + x + c
  4. D^3 x 3 - 2 x + x + c

Correct answer

C. - ^3 x 3 + x + x + c

Step-by-step solution

I = ^4 x , dx I = ^2 x ( ^2 x - 1) , dx I = ^2 x ^2 x , dx - ^2 x , dx I = ^2 x ^2 x , dx - ( ^2 x - 1) , dx Substituting x = t - ^2 x , dx = dt in the first integral: I = - t^2 , dt - (- x - x) + c I = - t^3 3 + x + x + c I = - ^3 x 3 + x + x + c Answer: - ^3 x 3 + x + x + c

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