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

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

Text Solution

Verified by Experts

`frac{1}{2} ln (frac{x^{2}-x+1}{x^{2}+x+1})+C`
Explanation:
` int frac{x^{2}-1}{x^{4}+x^{2}+1} cdot d x` `implies int frac{1-frac{1}{x^{2}}}{x^{2}+1+frac{1}{x^{2}}} cdot d x`
`implies int frac{(1-frac{1}{x^{2}}) cdot d x}{(x+frac{1}{x})^{2}-1}` ...
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