\(\int\left(1+\frac{x}{1 !}+\frac{x^2}{2 !}+\ldots \infty\right) d x=\)

\(\int\left(1+\frac{x}{1 !}+\frac{x^2}{2 !}+\ldots \infty\right) d x=\)
  1. \(\log (x+1)+c\)
  2. \(\frac{1}{x+1}+c\)
  3. \(e^x+c\)
  4. \(-e^{-x}+c\)

Solution

\(\begin{gathered} \int\left(1+\frac{x}{1 !}+\frac{x^2}{2 !}+\ldots \ldots\right) d x \\ =\int e^x \cdot d x=\left(e^x+c\right) \end{gathered}\)

Asked in: AP EAMCET 2020 (17 Sep Shift 1)

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