If int e^{x+tan^{-1} x} left(frac{x^2+2}{1+x^ | vedclass

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(C) Let $I = \int e^{x+	an^{-1} x} \left(\frac{x^2+2}{1+x^2}ight) dx$.Note that $\sec^2(	an^{-1} x) = 1 + x^2$.Let $g(x) = x + 	an^{-1} x$. Then

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$f(x)$ is strictly increasing on $\mathbb{R}$.

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(C) Let $I = \int e^{x+	an^{-1} x} \left(\frac{x^2+2}{1+x^2}ight) dx$.Note that $\sec^2(	an^{-1} x) = 1 + x^2$.Let $g(x) = x + 	an^{-1} x$. Then $g'(x) = 1 + \frac{1}{1+x^2} = \frac{1+x^2+1}{1+x^2} = \frac{x^2+2}{1+x^2}$.The integral becomes $\int e^{g(x)} g'(x) dx = e^{g(x)} + c$.Thus, $f(x) = x + 	an^{-1} x$.$f'(x) = 1 + \frac{1}{1+x^2}$.Since $1+x^2 > 0$ for all $x \in \mathbb{R}$, $f'(x) > 0$ for all $x \in \mathbb{R}$.Therefore, $f(x)$ is strictly increasing on $\mathbb{R}$.

If $\int e^{x+\tan^{-1} x} \left(\frac{x^2+2}{1+x^2}\right) dx = e^{f(x)} + c$, then which of the following is true?

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