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MHT CET202619 April 2026Morning ShiftMathematicsIndefinite IntegrationActual

If f(x) = 1 x and g(x) = 1 ( x)^2 , then the value of [f(x) - g(x)] ,dx is...

Options

  1. A( x)^2 + c
  2. Bx x + c
  3. Cx x + c
  4. D1 x + c

Correct answer

C. x x + c

Step-by-step solution

Let I = ( 1 x - 1 ( x)^2 ) dx Substitute x = t x = e^t dx = e^t dt I = e^t ( 1 t - 1 t^2 ) dt Using the standard integral e^t (h(t) + h'(t)) dt = e^t h(t) + c Here, h(t) = 1 t and h'(t) = - 1 t^2 I = e^t ( 1 t ) + c Substituting back t = x and e^t = x I = x x + c Answer: x x + c

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