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Evaluate: int frac{(x^2-1)}{(x^4+3x^2+1)...

Evaluate: `int frac{(x^2-1)}{(x^4+3x^2+1)tan^(-1)(x+1/x)}\ dx`

Text Solution

Verified by Experts

Let,
` I=int frac{x^{2}-1}{(x^{4}+3 x^{2}+1) tan ^{-1}(x+frac{1}{x})} d x`
On dividing numerator and denominator by `{x}^{2}`, we get
`I=int frac{1-frac{1}{x^{2}}}{(x^{2}+frac{1}{x^{2}}+3) tan ^{-1}(x+frac{1}{x})} d x`
...
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