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Evaluate: (i) 1/(1+x-x^2)\ dx (ii) int1/...

Evaluate: (i) `1/(1+x-x^2)\ dx` (ii) `int1/(2x^2-x-1)\ dx`

Text Solution

Verified by Experts

(i) `int frac{d x}{1+x-x^{2}}`
`=int frac{-d x}{x^{2}-x-1}`
`=int frac{-d x}{x^{2}-x+frac{1}{4}-frac{1}{4}-1}`
`=int frac{-d x}{(x-frac{1}{2})^{2}-frac{5}{4}}`
`=int frac{d x}{frac{5}{4}-(x-frac{1}{2})^{2}}`
`=int frac{d x}{(frac{sqrt{5}}{2})^{2}-(x-frac{1}{2})^{2}}`
...
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