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(1)/(x^(3)(1-x))...

`(1)/(x^(3)(1-x))`

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`int (1)/(x^(3)(1-x))dx=int ((1-x^(3))+x^(3))/(x^(3)(1-x))dx`
`=int [(1-x^(3))/(x^(3)(1-x))+(1)/(1-x)]dx`
`=int [((1-x)(1+x+x^(2)))/(x^(3)(1-x))+(1)/(1-x)]dx`
`=int [(1+x+x^(2))/(x^(3))+(1)/(1-x)]dx`
`=int((1)/(x^(3))+(1)/(x^(2))+(1)/(x)+(1)/(1-x))dx`
`=int x^(-3)dx+int x^(-2)dx +int(1)/(x)dx+int (1)/(1-x)dx`
`=(x^(-2))/(-2)+(x^(-1))/(-1)+log|x|+(log |1-x|)/(-1)+c`
`=log|(x)/(1-x)|-(1)/(2x^(2))-(1)/(x)+c`
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