$\int\left(\sum_{r=0}^{\infty} \frac{x^r 2^r}{r!}\right) d x=$

• A

  $e^x+c$
• B

  $\frac{-2}{1-2 x}+c$
• C

  $2 e^{2 x}+c$
• Correct answer
  D

  $\frac{\mathrm{e}^{2 \mathrm{x}}}{2}+\mathrm{c}$

Hence, the correct answer is option: 'D'.