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JEE Main202623 January 2026Evening ShiftMathematicsIndefinite IntegrationActual

Let I (x)= 3 d x (4 x+6) ( 4 x²+8 x+3 ) and I (0)= 3 4 +20 . If I ( 1 2 )= a 2 b + c , where a, b, c N , gcd (a, b)=1 , then a+b+c is equal to

Options

  1. A30
  2. B31
  3. C29
  4. D28

Correct answer

B. 31

Step-by-step solution

4x^2+8x+3 = (2x+1)(2x+3) and 4x+6 = 2(2x+3) . I(x) = 3 4 du u^ 3/2 u-2 where u = 2x+3 . Substituting u = 2 ^2 : I(x) = 3 4 + C = 3 4 2x+1 2x+3 + C . I(0) = 3 4 1 3 + C = 3 4 + C = 3 4 + 20 C = 20 . I ( 1 2 ) = 3 4 2 4 + 20 = 3 4 2 + 20 = 3 2 8 + 20 . a = 3, b = 8, c = 20 , (3,8) = 1 . a+b+c = 31 .

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