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Evaluate: int(2x)/(x^3-1)\ dx...

Evaluate: `int(2x)/(x^3-1)\ dx`

Text Solution

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`I=int frac{2 x d x}{x^{3}-1} `
`=int frac{2 x d x}{(x-1)(x^{2}+x+1)} `
`text { Let } frac{2 x}{(x-1)(x^{2}+x+1)}=frac{A}{x-1}+frac{B x+C}{x^{2}+x+1} `
`Rightarrow frac{2 x}{(x-1)(x^{2}+x+1)}=frac{A(x^{2}+x+1)+(B x+C)(x-1)}{(x-1)(x^{2}+x+1)} `
`Rightarrow 2 x=A(x^{2}+x+1)+B x^{2}-B x+C x-C `
`Rightarrow 2 x=(A+B) x^{2}+(A-B+C) x+A-C`
Equating coefficients of like terms
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