# Partial integration

if you are not lazy, you will answer what is the general antiderivative of (2x^3+3x^2+x-1)/((x+1)*((x^2+2x+2)^2))

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Originally posted by kallazans
S((2x^3+3x^2+x-1)/(x+1)(x^2+2x+2))dx!
are you like this?

I don't understand your question, and your equation is unclear. Do you mean

$$\int ((2x^3+3x^2+x-1)/(x+1)(x^2+2x+2)) {\rm d}x =$$

$$\int\frac{2x^3+3x^2+x-1}{x+1}(x^2+2x+2){\rm d}x =$$

$$-x+\frac{x^2}{2}+2x^3+\frac{5x^4}{4}+\frac{2x^5}{5}-\log(1+x)$$

or do you mean

$$\int ((2x^3+3x^2+x-1)/\left((x+1)(x^2+2x+2))\right) {\rm d}x =$$

$$\int\frac{2x^3+3x^2+x-1}{(x+1)(x^2+2x+2)}{\rm d}x =$$

$$2x-\arctan(1+x)-\log(1+x)-\log(2+(2+x)x)$$