Using the method of partial fractions show your users that ∫ dx/x^2(x-2) = -1/4In(x) + 1/2x + 1/4In (x-2) + constant
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You need to use partial fraction decomposition to write the given integral as a sum (difference) of a simpler integrals such that:
`1/(x^2(x-2)) = A/x + B/x^2 + C/(x-2)`
`1 = Ax(x-2) + B(x-2) + Cx^2`
`1 = Ax^2 - 2Ax + Bx - 2B + Cx^2`
`1 =x^2(A+C) + x(-2A + B) - 2B`
Equating the coefficients of like powers yields:
`A+C = 0 => C = -A`
`-2A...
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