∫$$01$$ $$tan$$−$$1$$⁡$$1x2$$−$$x+1$$ is equal to

Question

∫$$01$$ $$tan$$−$$1$$⁡$$1x2$$−$$x+1$$ is equal to

Infinity Learn · Accepted Answer

∫$$01$$ $$tan$$−$$1$$⁡$$1x2$$−$$x+1dx=$$∫$$01$$ $$tan$$−$$1$$⁡x−(x$$−$$1)1+x(x$$−$$1)=$$∫$$01$$ $$tan$$−$$1$$⁡xdx−∫$$01$$ $$tan$$−$$1$$⁡$$(x$$−$$1)dx=$$∫$$01$$ $$tan$$−$$1$$⁡$$xdx+$$∫$$01$$ $$tan$$−$$1$$⁡$$(1$$−$$1+x)dx=$$∫$$01$$ $$tan$$−$$1$$⁡$$xdx+$$∫$$01$$ $$tan$$−$$1$$⁡$$xdx=2$$∫$$01$$ $$tan$$−$$1$$⁡$$xdx=2xtan$$−$$1$$⁡x−∫$$x1+x2dx01=2xtan$$−$$1$$⁡x−$$12log$$⁡$$1+x201=21tan$$−$$1$$⁡$$1$$−$$12log$$⁡$$(2)−$$0$$−$$12log$$⁡$$1=2$$$$π$$$$4$$−$$12log$$⁡$$2$$−$$0=$$π$$2$$−log⁡$$2$$

$\int_{0}^{1} \tan^{- 1} (\frac{1}{x^{2} - x + 1})$ is equal to

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∫01 tan−1⁡1x2−x+1 is equal to

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$\int_{0}^{1} \tan^{- 1} (\frac{1}{x^{2} - x + 1})$ is equal to