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Evaluate: int(x^2)/(x^4+x^2-2)\ dx...

Evaluate: `int(x^2)/(x^4+x^2-2)\ dx`

Text Solution

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Let `I=int frac{x^{2}}{x^{4}+x^{2}-2} d x`
We express
`frac{x^{2}}{x^{4}+x^{2}-2}=frac{x^{2}}{x^{4}+2 x^{2}-x^{2}-2} `
`=frac{x^{2}}{(x^{2}+2)(x^{2}-1)} `
`=frac{A}{x^{2}+2}+frac{B}{x^{2}-1} `
`Rightarrow x^{2}=A(x^{2}-1)+B(x^{2}+2)`
Equating the coefficients of `x^{2}` and constants, we get
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