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JEE Main201911 Jan 2019Evening ShiftMathematicsIndefinite IntegrationActual

If x+1 2 x-1 ~d x=f(x) 2 x-1 + C , where C is a constant of integration, then f(x) is equal to:

Options

  1. A1 3 (x+1)
  2. B2 3 (x+2)
  3. C2 3 (x-4)
  4. D1 3 (x+4)

Correct answer

D. 1 3 (x+4)

Step-by-step solution

Let I= x+1 2 x-1 d x Put 2 x-1 =t array l 2 x-1=t² d x=t d t I= (t²+3 ) 2 d t= t³ 6 + 3 t 2 +C = (2 x-1)^ 3 2 6 + 3 2 (2 x-1)^ 1 2 +C = 2 x-1 ( x+4 3 )+C =f(x) 2 x-1 +C array Hence, f(x)= x+4 3

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