Question

Question #38661

Answer 1

`g(x)={7-6x^3+2x^6}/x^6`

by splitting the quotient into smaller quotients,

`=7/x^6-{6x^3}/x^6+{2x^6}/x^6`

by rewriting and cancelling out common factors,

`=7x^{-6}-6x^{-3}+2`

So, the most general antiderivative is

`G(x)=7{x^{-5}}/{-5}-6{x^{-2}}/{-2}+2x+C`

by cleaning up a bit,

`=-7/5x^{-5}+3x^{-2}+2x+C`

---

I hope that this was helpful.