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JEE Main201912 Jan 2019Morning ShiftMathematicsIndefinite IntegrationActual

The integral ∫ c o s lnx d x , is equal to

Options

  1. Ax 2 cos lnx - sin ln x + C
  2. Bx cos lnx - sin ln x + C
  3. Cx cos lnx + sin ln x + C
  4. Dx 2 cos lnx + sin ln x + C

Correct answer

D. x 2 cos lnx + sin ln x + C

Step-by-step solution

Given, I = ∫ c o s ln x d x Let, ln x = t ⇒ x = e t ⇒ d x = e t d t ∴ I = ∫ e t c o s t d t ∫ e t cos t d t = 1 2 ∫ e t c o s t + s i n t + c o s t - s i n t d t ∫ e t cos t   d t = 1 2 e t cost + s i n t + C , where C is the constant of integration. = x 2 cos lnx + s i n ln x + C .

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