# f(x) = 6x^2 -8x +3

how would I find the most general antiderivative of the function. I also have to check my answer by differentiation.

Would I have to find the derivative first? (I got 12x -8)
What are the steps to solving a problem like this?

No, don't do the derivative first. Do that on the integral, to check your answer.

I use the word "integral" for what you are calling "antiderivative". You can say I am old-fashioned, but I don't see a need for a longer word.

The general rule for integrating any
a x^n term
is that the integral is
a x^(n+1)/(n+1)
When you have a polynomial, as you do here, the integral is the sum of the integrals of the terms.

The first term of the integral is
6 x^3/3 = 2 x^3. Take the derivative of that and you get the original 6 x^2 back, so it is the right answer.

Now you do the other terms, and add them up.

Remember that the most general integral has an arbitrary constant term added.

## To find the most general antiderivative of the function f(x) = 6x^2 - 8x + 3, you can follow these steps:

1. Apply the power rule for integration to each term individually. The power rule states that the integral of a x^n term is (a/(n+1)) * x^(n+1).

2. For the first term, 6x^2, you can apply the power rule to get (6/(2+1)) * x^(2+1) = 2x^3.

3. For the second term, -8x, you can apply the power rule to get (-8/(1+1)) * x^(1+1) = -4x^2.

4. For the third term, 3, you can consider it as 3x^0 and apply the power rule to get (3/(0+1)) * x^(0+1) = 3x.

5. Now, you can sum up the results from steps 2-4 to obtain the most general antiderivative:
2x^3 - 4x^2 + 3x + C, where C is the constant of integration.