int {left( {1 + x + frac{{{x^2}}}{{2!}} + fra | vedclass

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Question

(B) The given expression inside the integral is the Taylor series expansion for the exponential function $e^x$. We know that $e^x = 1 + x + \frac{x^2}

Vedclass · Accepted Answer

${e^x} + c$

Vedclass · Answer

(B) The given expression inside the integral is the Taylor series expansion for the exponential function $e^x$. We know that $e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots$. Substituting this into the integral,we get: $\int {\left( {1 + x + \frac{{{x^2}}}{{2!}} + \frac{{{x^3}}}{{3!}} + \dots} \right) dx} = \int {{e^x} dx}$. The integral of $e^x$ with respect to $x$ is $e^x + c$. Therefore,the correct option is $B$.

$\int {\left( {1 + x + \frac{{{x^2}}}{{2!}} + \frac{{{x^3}}}{{3!}} + \dots} \right) dx} = $

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