Partial Fraction: Solving x^3+1/x^2+4

[tnutty]

Homework Statement

x^3+1 / x^2+4

Homework Equations

The Attempt at a Solution

after using long division i get : x + -(4x-1) / (x^2+4)

then using partial fraction :

-4x-1 / x^2+4 = bx+c / x^2+4

then i am stuck because if what i have
is correct then they both are the same and in the same form.

 

[gabbagabbahey]

-4x-1 / x^2+4 = bx+c / x^2+4

then i am stuck because if what i have
is correct then they both are the same and in the same form.

$$-\frac{4x-1}{x^2+4}=\frac{1}{x^2+4}-\frac{4x}{x^2+4}$$...

 

[Dick]

Once you gotten to (-4x-1)/(x^2+4) you probably want to leave the partial fractions trail. Split it into -4x/(x^2+4) and -1/(x^2+4). The first one is a simple substitution. I'm going to guess the second one might be something related to arctan(x)? Try a trig substitution.