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COMEDK20269 May 2026Evening ShiftMathematicsIndefinite IntegrationActual

( ^6 x + ^6 x + 3 ^2 x ^2 x ) , dx =

Options

  1. A- 3 2 2x + C
  2. B2 3 x + C
  3. C3 2 2x + C
  4. Dx + C

Correct answer

D. x + C

Step-by-step solution

Let I = ( ^6 x + ^6 x + 3 ^2 x ^2 x) , dx Using the algebraic identity a^3 + b^3 = (a+b)^3 - 3ab(a+b) , we can write: ^6 x + ^6 x = ( ^2 x + ^2 x)^3 - 3 ^2 x ^2 x ( ^2 x + ^2 x) Since ^2 x + ^2 x = 1 , we get: ^6 x + ^6 x = 1 - 3 ^2 x ^2 x Substituting this back into the integrand: ^6 x + ^6 x + 3 ^2 x ^2 x = 1 - 3 ^2 x ^2 x + 3 ^2 x ^2 x = 1 Therefore, the integral becomes: I = 1 , dx = x + C Answer: x + C

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