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int (1-x^2)/(x(1-2x)) dx=...

`int (1-x^2)/(x(1-2x)) dx=`

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(2)x+log |x|-(3)/(4)log |1-2x|+C`
`((1-x^(2)))/(x(1-2x))=((-x^(2)+1))/((-2x^(2)+x))={(1)/(2)+((1-(1)/(2x)))/(x(1-2x))}.`
`Let ((1-(1)/(2x)))/(x(1-2x))=(A)/(x)+(B)/((1-2x))."then " (1-(1)/(2x))-=A(1-2x)+Bx.`
`(x=0impliesA=1)and (x=(1)/(2)impliesb=(3)/(2))`
`therefore I=int{(1)/(2)+(1)/(x)+(3)/(2(1-2x))}dx.`
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