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Evaluate: int(x^2)/(1-x^4)\ dx...

Evaluate: `int(x^2)/(1-x^4)\ dx`

Text Solution

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