Hi, I need to use the anti-derivative for the function of f(x) = -4/3(x^3-1). I need to get to the first function equation. However, there is a slight, and by slight I mean major, issue. I do not know and was not taught how to use the anti-derivative law with fractions. I keep on getting closer to the answer but cannot get it. This is what I got for f(x') = 2/3(x^-3 - 1)^2.
What should I do next? f(x') is clearly incorrect.
Edit. I also got f(x') = 1/2(x^3 1)^-4. This is much closer, but still wrong.
I am still not getting the correct answer. I have no idea what to do because I have a variable with an exponent on the function. Anyways, the function should be f(x) = (-4/3) (x^(-3)-1). In other words, the function that has a variable on it should be negative and not positive.
Now, assuming that your integral is ...
Now integrate that stuff term by term using the rule you know . It doesn't make any difference if your exponent is negative (except if your exponent is -1).