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Evaluate: int(x^2)/((x^2+a^2)(x^2+b^2))...

Evaluate: `int(x^2)/((x^2+a^2)(x^2+b^2))dx`

Text Solution

Verified by Experts

Let `I=int frac{x^{2}}{(x^{2}+a^{2})(x^{2}+b^{2})} d x`
We express
`frac{x^{2}}{(x^{2}+a^{2})(x^{2}+b^{2})}=frac{A}{x^{2}+a^{2}}+frac{B}{x^{2}+b^{2}} `
`Rightarrow x^{2}=A(x^{2}+b^{2})+B(x^{2}+a^{2})`
Equating the coefficients of `x^{2}` and constants, we get
`1=A+B` and `0=b^{2} A+a^{2} B`
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