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

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Question

(A) We know that the Taylor series expansion for the exponential function $e^x$ is given by: $e^x = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!}

Vedclass · Accepted Answer

$e^x + c$

Vedclass · Answer

(A) We know that the Taylor series expansion for the exponential function $e^x$ is given by: $e^x = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots \infty$ Substituting this into the integral,we get: $\int \left(1 + \frac{x}{1!} + \frac{x^2}{2!} + \dots \infty \right) dx = \int e^x dx$ The integral of $e^x$ with respect to $x$ is $e^x + c$,where $c$ is the constant of integration. Therefore,the final answer is $e^x + c$.

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

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