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JEE Main20257 Apr 2025Morning ShiftMathematicsDefinite IntegrationActual

The integral ₀^ (x+3) x 1+3 ^2 x d x is equal to :

Options

  1. A3 ( +1)
  2. B3 ( +2)
  3. C3 3 ( +6)
  4. D2 3 ( +4)

Correct answer

C. 3 3 ( +6)

Step-by-step solution

aligned & I= ₀^ (x+3) x 1+3 ^2 x d x & I= ₀^ ( -x+3) x (1+3 ^2 x ) d x & 2 I= ₀^ ( +6) x d x (1+3 ^2 x ) =2 ₀^ / 2 ( +6) x (1+3 ^2 x ) & I= ₀^ / 2 ( +6) x d x (1+3 ^2 x ) = 3 3 ( +6) & 3 x=t & 3 x=d t aligned

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