∫etan−$$1$$⁡$$x1+x+x2$$⋅dcot−$$1$$⁡x is equal to

Correct option is 3−xetan−1⁡x+C

Questions

$\int e^{\tan^{- 1} x} (1 + x + x^{2}) \cdot d (\cot^{- 1} x) is equal to$

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−etan−1⁡x+C

etan−1⁡x+C

−xetan−1⁡x+C

xetan−1⁡x+C

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detailed solution

Correct option is C

I=∫etan−1⁡x1+x+x2⋅−11+x2dx=−∫etan−1⁡x1+x1+x2dx=−∫etan−1⁡xdx−∫x⋅etan−1⁡x1+x2dx integration by parts=−∫etan−1⁡xdx−x⋅etan−1⁡x+∫etan−1⁡xdx+C=−x⋅etan−1⁡x+C

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∫etan−1⁡x1+x+x2⋅dcot−1⁡x is equal to

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$\int e^{\tan^{- 1} x} (1 + x + x^{2}) \cdot d (\cot^{- 1} x) is equal to$