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$\int \frac{e^{\tan^{- 1} x}}{1 + x^{2}} dx$ is equal to

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−etan−1⁡x+C

etan−1⁡x+C

tan−1⁡x+C

−tan−1⁡x+C

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detailed solution

Correct option is B

Here, the given integrand is of the form ,ef(x), f ' (x),so we use substitution method to integrate it. ∫etan−1⁡x1+x2dx Let tan−1⁡x=t⇒11+x2=dtdx⇒ dx=1+x2dt∴ ∫etan−1⁡x1+x2dx=∫et1+x21+x2dt=∫etdt=et+C=etan−1⁡x+C

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∫etan−1⁡x1+x2dx is equal to

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$\int \frac{e^{\tan^{- 1} x}}{1 + x^{2}} dx$ is equal to