Long division polynomial Integral not sure what long division is going on here .. probably just forgetting something

Question

anonymous · Answer

$$\int \frac{dx}{x^2-x^3+\frac{5}{12}x^4-\frac{7}{72}x^5+....}$$

anonymous · Answer

it goes to then next step saying long after long division

anonymous · Answer

the way my teacher did it was he had the outside the bottom and the inside 1... but that just seems weird to me

unklerhaukus · Answer

i can't even see the pattern in the denominator yet, 
by i guess you can factor out $x^2$

anonymous · Answer

still not seeing what long division is going lol sorry i know it's going to be

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