Answer:
2x³/3 +2x²-6x+C
Step-by-step explanation:
Given the function
f(x) = (x + 3)(2x − 2)
Expand first
f(x) = 2x²-2x+6x-6
f(x) = 2x²+4x-6
Integrate the resulting function
Integrate (2x²+4x-6) =2x³/3 + 4x²/2 - 6x + C
= 2x³/3 +2x²-6x+C
For us to check the correctness, we need to differentiate the answer and we must arrive back at the question
On differentiating 2x³/3 +2x²-6x
3(2/3)x² + 2(2)x¹ -6
= 6/3x²+4x-6
= 2x²+4x-6
This shows the answer is correct.
The correct anti derivative of the function is 2x³/3 +2x²-6x+C
