The integral that I am trying to evaluate is $\int \frac{7-x}{x^3-x^2-x-2}dx.$ Here is the Wolfram Alpha link: W|A Link
Thanks to all who take a look!
The integral that I am trying to evaluate is $\int \frac{7-x}{x^3-x^2-x-2}dx.$ Here is the Wolfram Alpha link: W|A Link
Thanks to all who take a look!
The polynomial $x^{3}-2x^{2}-x-2$ does not factor nicely at all, so this problem will have an incredibly ugly and complicated solution as you saw on Wolfram Alpha. There is no way to get around this.
However, I'll assume this is for a calculus course you are taking. Then, I believe there there is a typo and that the denominator should be $x^{3}-2x^{2}-x+2$ (the last sign should be $+$ instead of $-$). This polynomial factors very nicely as $(x-2)(x-1)(x+1).$ Then in this case partial fractions yields $\frac{7-x}{x^{3}-2x-x+2}=\frac{-3}{x-1}+\frac{4}{3(x+1)}+\frac{5}{3(x-2)},$
so that
$\int\frac{7-x}{x^{3}-2x-x+2}dx=-3\ln|x-1|+\frac{4}{3}\ln|x+1|+\frac{5}{3}\ln|x-2|+C.$
Hope that helps,