Question

What is `int g(x) = (5-6x^3) / x dx`?

Answer 1

`int(5-6x^3)/xdx = 5ln(x) - 2x^3 + c`

Explanation:

Umm, you kinda mixed up the notation there buddy.

`g(x) = int(5-6x^3)/xdx`

Means which function is `g(x)`, if it is that integral

Whereas

`int(g(x))dx = (5 - 6x^3)/xdx`

Seems to imply that the integral of `g(x)` is that, so which function is `g(x)`

I'm guessing you mean the first one, which the way you wrote isn't technically wrong but it's a bit confusing. In that case, we have

`int(5-6x^3)/xdx = int(5/x - 6x^2)dx`
`int(5/x - 6x^2)dx = int(5/x)dx - int(6x^2)dx`
`int(5/x)dx - int(6x^2)dx = 5intdx/x - 6intx^2dx`
`5intdx/x - 6intx^2dx = 5(ln(x)) - 6(x^3/3) + c`
`int(5-6x^3)/xdx = 5ln(x) - 2x^3 + c`