The integral ∫etan−$$1$$⁡$$x1+x+x21+x2dx$$ is equal to

Correct option is 3xetan−1⁡x+C

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The integral $\int e^{\tan^{- 1} x} (\frac{1 + x + x^{2}}{1 + x^{2}}) d x$ is equal to

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etan−1⁡x1+x2+C

xetan−1⁡x1+x2+C

xetan−1⁡x+C

none of these

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detailed solution

Correct option is C

Putting tan−1⁡x=u, we have dx1+x2=du∫etan−1⁡x1+x+x21+x2dx=∫eu1+tan⁡u+tan2⁡udu=∫eusec2⁡u+tan⁡udu=tan⁡ueu+C=xetan−1⁡x+C. (using ∫exf(x)+f′(x)dx=exf(x)+C )

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The integral ∫etan−1⁡x1+x+x21+x2dx is equal to

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The integral $\int e^{\tan^{- 1} x} (\frac{1 + x + x^{2}}{1 + x^{2}}) d x$ is equal to