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JEE Main202118 Mar 2021Morning ShiftMathematicsIndefinite IntegrationActual

The integral ∫ ( 2 x - 1 ) cos ( 2 x - 1 ) 2 + 5 4 x 2 - 4 x + 6 d x is equal to (where c is a constant of integration)

Options

  1. A1 2 sin ( 2 x - 1 ) 2 + 5 + c
  2. B1 2 cos ( 2 x + 1 ) 2 + 5 + c
  3. C1 2 cos ( 2 x - 1 ) 2 + 5 + c
  4. D1 2 sin ( 2 x + 1 ) 2 + 5 + c

Correct answer

A. 1 2 sin ( 2 x - 1 ) 2 + 5 + c

Step-by-step solution

∫ ( 2 x - 1 ) cos ( 2 x - 1 ) 2 + 5 ( 2 x - 1 ) 2 + 5 d x ( 2 x - 1 ) 2 + 5 = t 2 2 2 x - 1   2 d x = 2   t d t 2 t 2 - 5 d x = t d t So ∫ t 2 - 5 cos t 2 t 2 - 5 d t = 1 2 sin t + c = 1 2 sin ( 2 x - 1 ) 2 + 5 + c

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