dx-x-2-x-1-

Question Number 20238 by tammi last updated on 24/Aug/17

\int \frac{d x}{x^{2} - x + 1}

Commented by tammi last updated on 24/Aug/17

t h i s a n s w e r i s \frac{2}{\sqrt{3}} \tan^{- 1} (\frac{2 x - 1}{\sqrt{3}}) + c

i k n o w t h e a n s w e r b u t c a n n o t s o l v e t h i s p r b l m . . h e l p

Answered by $@ty@m last updated on 25/Aug/17

= \int \frac{d x}{x^{2} - 2 . \frac{1}{2} x + {(\frac{1}{2})}^{2} - {(\frac{1}{2})}^{2} + 1}

= \int \frac{d x}{{(x - \frac{1}{2})}^{2} + {(\frac{\sqrt{3}}{2})}^{2}}

= \frac{2}{\sqrt{3}} {t a n}^{- 1} \frac{x - \frac{1}{2}}{\frac{\sqrt{3}}{2}}

= \frac{2}{\sqrt{3}} {t a n}^{- 1} \frac{2 x - 1}{\sqrt{3}} + C

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