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(2)/((1-x)(1+x^(2)))...

`(2)/((1-x)(1+x^(2)))`

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`" Let " (2)/((1-x)(1+x^(2)))=(A)/(1-x)+(Bx+C)/(1+x^(2))`
`:. (2)/((1-x)(1+x^(2)))=(A(1+x^(2))+(Bx+C)(1-x))/((1-x)(1+x^(2)))`
`rArr 2=A (1+x^(2)) +(Bx+C) (1-x)`
`x=1 " then " 2=A(1+1)+0 rArr A=1`
`x=0 " then " 2=A+c`
`rArr C=2 -A =2-1 =1`
Equating the coefficients of `x^(2) ,0=A-B`
`rArr B=A=1`
`:. int(2)/((1-x)(1+x^(2)))dx = int{(1)/(1-x)+(x+1)/(x^(2)+1)}dx`
` = int (1)/(1-x)dx +(1)/(2) int(2x)/(x^(2)+1)dx + int (1)/(x^(2)+1)dx`
`=-log |1-x|+(1)/(2) log (1+x^(2))+tan^(-1) x+C_(1)`
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