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helpppp please

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helpppp please

evaluate the integral dx/(1-x^3)


first make this equivalence change
3/(1-x^3)=1/(1-x)+(x+1/2)/(1+x+x^2)+(3/2)/(1+x+x^2)
and each term is integrable
1) integral 1/(1-x) dx=-ln(1-x)
2) integral (x+1/2)/(1+x+x^2) dx=(1/2)*ln(x^2+x+1)
3) integral (3/2)/(1+x+x&2) dx=sqrt(3)*arctan[(x+1/2)*2/sqrt(3)]
therefore the answer is
(1/3)*{-ln(1-x)+(1/2)*ln(x^2+x+1)+sqrt(3)*arctan[(x+1/2)*2/sqrt(3)]}

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