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Integrate the functions1/(x-x^3)...

Integrate the functions`1/(x-x^3)`

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`int (1)/(x-x^(3)) dx= int(1)/(x(1-x^(2)))dx`
`=int (1)/(x(1-x)(1+x))dx" "......(1)`
` " Let " (1)/(x(1-x)(1+x)) =(A)/(x)+(B)/((1-x))+(C)/((1-x))`
`rArr 1=A(1+x)(1-x)+B(x)(1+x)+C(x)(1-x)`
`x=-1 " then " 1=0 +0+ C(-1)(2)rArr B=(1)/(2)`
`x=1 " then " 1=A (1) (1)+0 +0 rArr A=1`
`:. int (1)/(x(1-x^(2)))dx`
`=int(1)/(x) dx+ (1)/(2) int (1)/(1-x)dx-(1)/(2) int (1)/(1+x) dx`
`=log |x| -(1)/(2) log |1-x| -(1)/(2) log |1+x|+C`
`=(1)/(2) log |(x^(2))/(1-x^(2))|+C`
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