Question

Question #31800

Answer 1

`-3x^2-3x-5lnabsx+C`

Explanation:

`int` `(-6x^2-3x-5)/x dx`

We can rewrite the integral as:

`int` `((-6x^2)/x-(3x)/x-5/x)dx`

And simplify:

`int` `(-6x-3-5/x)dx`

We can now take each integral separately. It may help re-visualize the integral as:

`int` `-6xdx` `-int` `3dx` `-int` `5/xdx`

So the antiderivative is

`-6` `1/2x^2-3x-5lnabsx`

Simplifying...

`-3x^2-3x-5lnabsx+C`

Since you asked for the most general antiderivative, we add the constant `C` to represent any constant which when we take its derivative, will always be `0`