Question

What is the antiderivative of `(7x^3 - 6)/x^2`?

Answer 1

`F(x)=7/2x^2+6/x+c`

Explanation:

The first step here is to divide out the function.

`(7x^3-6)/x^2=(7x^3)/x^2-6/x^2=7x-6x^-2`

`rArrint(7x^3-6)/x^2 dx=int(7x-6x^-2)dx`

Integrate using the `color(blue)" power rule"`

`int(ax^n)=(ax^(n+1))/(n+1)`

`rArrint(7x-6x^-2)dx=7/2x^2+6x^-1+c`

`rArrF(x)=7/2x^2+6/x+c`