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.
I have now had to waste two posts telling you how to go about answering your question because I have tried to translate (wrongly) what you have written. I suggest you learn some basic LaTeX so that you can avoid frustrating the people here who are trying to help you.
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).