Question

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

Answer 1

`g(x) = (3 - 6x^3 + 2x^6) / x^6`

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

`= 3x^-6 -6x^-3+2`

Use the power rule to find the antiderivative:

`(3x^((-6+1)))/((-6+1)) - (6x^((-3+1)))/((-3+1))+2x/1`

`= (3x^-5)/-5 - (6x^-2)/-2 + 2x`

`= -3/(5x^5) + 6/(2x^2) + 2x`

Get a common denominator to write as a single ratio if you like.