`f(x) = (x^5 - x^3 + 2x)/(x^4)` Find the most general antiderivative of the function.

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to evaluate the most general antiderivative, using the following rule, such that:

`int f(x) dx = F(x) + c`

`int (x^5 - x^3 + 2x)/(x^4) dx = int(x^5)/(x^4) dx - int (x^3)/(x^4)dx + int (2x)/(x^4)dx`

`int (x^5 - x^3 + 2x)/(x^4) dx = int xdx - int (1/x)dx + int 2/(x^3)dx`

`int (x^5 - x^3 + 2x)/(x^4) dx = x^2/2 - ln |x| - 1/x^2 + c`

Hence, evaluating the most general antiderivative yields `F(x) = x^2/2 - ln |x| - 1/x^2 + c.`