Integrate 1/ (-v^2-v+3) please

Question

mathmale · Answer

Looks like a good candidate for the partial fraction method of separating the integrand into easier-to-integrate terms.  Are you familiar with partial fractions?

anonymous · Answer

i don't see how it can be solved using partial fractions. it can't be factored
anyways, i wrote down the wrong problem which led me to this mess

mathmale · Answer

Why not start over again?  Post the problem on which you'd like to focus.

anonymous · Answer

$$\int\limits_{}^{}\frac{1}{-v^2-v+3}dv$$
right?

anonymous · Answer

@kimmy0394

anonymous · Answer

yes sayakdbz

dumbcow · Answer

hmm how about completing the square, then a trig substitution

$$- \int\limits \frac{1}{(v+\frac{1}{2})^2 -\frac{13}{4}}$$

mathmale · Answer

Kimmy:  I'd thought you said you'd posted the wrong problem.  Please let those helping you know on what you want to focus.

anonymous · Answer

ok here's the problem: Use the method discussed under “Homogeneous Equations”
to solve (3x^2 -y^2)dx + (xy-x^3y^-1) =0

anonymous · Answer

a'ight. hold on. u gotta make the denominator a perfect square just as @kimmy0394

anonymous · Answer

*just as @dumbcow  mentioned

mathmale · Answer

Kimmy:  Please warn the others that your focus has shifted to solving this differential equation.

anonymous · Answer

so i'm just gonna award dumbcow the medal for my original question and i'll close it and post another. Thank you sayakdbz for your input as well