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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{(x^{2}+1)}{(x^{4}+x^{2}+1)}=frac{(1+frac{1}{x^{2}})}{(x^{2}+1+frac{1}{x^{2}})}=frac{(1+frac{1}{x^{2}})}{(x-frac{1}{x})^{2}+(sqrt{3})^{2}} `
Put
`(x-frac{1}{x})=t` and `(1+frac{1}{x^{2}}) d x=d t `
`therefore I=int frac{d t}{t^{2}+(sqrt{3})^{2}}`
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