Solution to Answer:

y= (2x^2)/2 + 4x + C

Therefore:

y= x^2 + 4x + C

Steps on how to do C1 Integration

y = a*x^n

y = a*x^n is y = (a/n+1)*x^(n+1)

Therefore, our final answer in this case is y = (a/n+1)*x^(n+1) + C.

We add the integration constant as when we defrentiate a function f(x) and have a constant in the equation, the constant goes. therfore when integrating we do the opposite of integration and hence add the integration constant C.

Differentiating the expression y=2x+2.
The answer would be f'(x)= 2
Now when you integrate the expression f'(x)
The answer would be y=2x
Something is missing?
As we don't know if there is a constant when we integrate and we also don't know its value we put the integration constant "C" to show the fact that there might be a constant.
The correct answer for the integration of f'(x)=2 would be y=2x+c where c=2 in this case.

integrate x^2 + ln(x)

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Integrate this funtion f'(x)=2x +4 with respect to x (C1 integration)