Integral Calculus Antiderivative Question

[xskull]

Homework Statement

Find the antiderivative of:

\int \frac{dx}{x^3 - 2x^2 + 4x - 18}

Homework Equations

This was asked in my Calculus II class right after we finished dealing with Solving for
Integrals using Partial Fractioning.

The Attempt at a Solution

This is really more of an algebra question as all I need to know are the factors
of the denominator to be able to start applying Partial Fractions.

I've been browsing the internet for ways to factor this. I read about the http://en.wikipedia.org/wiki/Rational_root_theorem"
and used Synthetic Division for every root that the theorem gave me, but to no avail.

I also tried simplifying the equation, although it didn't looked simplified, but letting
x = y + 2/3
then letting
y = z - (8/3)/9z
to produce the equation: 729z^6 - 11610z^3 - 512
Doing the above doesn't help me much, though.

Someone advised me to apply Numerical Integration, I don't know why since we haven't discussed about it yet.

I'm starting to wonder if this can be solved. Please advise.

 

[Mentallic]

Homework Statement

Find the antiderivative of:

\int \frac{dx}{x^3 - 2x^2 + 4x - 18}

Homework Equations

This was asked in my Calculus II class right after we finished dealing with Solving for
Integrals using Partial Fractioning.

The Attempt at a Solution

This is really more of an algebra question as all I need to know are the factors
of the denominator to be able to start applying Partial Fractions.

I've been browsing the internet for ways to factor this. I read about the http://en.wikipedia.org/wiki/Rational_root_theorem"
and used Synthetic Division for every root that the theorem gave me, but to no avail.

I also tried simplifying the equation, although it didn't looked simplified, but letting
x = y + 2/3
then letting
y = z - (8/3)/9z
to produce the equation: 729z^6 - 11610z^3 - 512
Doing the above doesn't help me much, though.

Someone advised me to apply Numerical Integration, I don't know why since we haven't discussed about it yet.

I'm starting to wonder if this can be solved. Please advise.

I'm curious, what compelled you to make those substitutions for x,y,z? And now let w=z³...