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MHT CET202620 April 2026Morning ShiftMathematicsIndefinite IntegrationActual

(e^ ( x) + x ) x , dx =

Options

  1. Ax( x + x) + ( x - x) + c
  2. Bx( x - x) + ( x - x) + c
  3. Cx( x + x) + ( x + x) + c
  4. Dx( x - x) + ( x + x) + c

Correct answer

D. x( x - x) + ( x + x) + c

Step-by-step solution

Using the property e^ f(x) = f(x) , the given integral simplifies to: x( x + x) dx Applying integration by parts, taking x as the first function and ( x + x) as the second function: x( x + x) dx = x ( x + x) dx - ( d dx (x) ( x + x) dx ) dx = x( x - x) - 1 ( x - x) dx = x( x - x) - (- x - x) + c = x( x - x) + ( x + x) + c Answer: x( x - x) + ( x + x) + c

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