what is the integral of x/(x^3 -1) i got an answer of ln(x-1)/3 - ln(2((x^2 + x + 1)^(1/2))/(3)^(1/2)) + ((3)^(1/2))arctan(2(x+(1/2))/((3)^(1/2))) + C but im not sure if thats at all right.. any help would be appreciated
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$\displaystyle \frac{x}{x^3-1}=\frac{x}{(x-1)(x^2+x+1)}=\frac{A}{x-1}+\frac{Bx+C}{x^2+x+1}$ $\displaystyle x=(A+B)x^2+(A-B+C)x+A-C\Rightarrow\left\{\begin{array}{lll}A+B=0\\A-B+C=1\\A-C=0\end{array}\right.$ Now find A, B, C.
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