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JEE Main20238 Apr 2023Evening ShiftMathematicsIndefinite IntegrationActual

The integral ∫ x 2 x + 2 x x log 2 x d x is equal to

Options

  1. Ax 2 x + 2 x x + C
  2. Bx 2 x - 2 x x + C
  3. Cx 2 x log 2 x 2 + C
  4. Dx 2 x log 2 2 x + C

Correct answer

A. x 2 x + 2 x x + C

Step-by-step solution

Given, I = ∫ x 2 x + 2 x x log 2 x   d x Now, Let x 2 x = t ⇒    x log 2 x 2 = log 2 t ⇒    x log e x 2 · log 2 e = log e t · log 2 e On differentiating both sides we get : log e x 2 + x · 2 x · 1 2 = 1 t d t d x ⇒ log e x 2 + 1 = 1 t d t d x Then solution is not possible as there is no proper substitution. Note: This question was bonus in Jee Mains 2023 April session.

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