Which of the following integrals represents the length of the curve $y=2^x,\;\;0 \le x \le 3?$

A. $\displaystyle \int_{0}^{\,3} {\sqrt{1+(\ln2)^2 2^{2} }}\,dx$
B. $\displaystyle \int_{0}^{\,3} {\sqrt{1+2(\ln2)^2 2^{x} }}\,dx$
C. $\displaystyle \int_{0}^{\,3} {\sqrt{1+(\ln2)^2 2^{2x}}}\,dx$
D. $\displaystyle \int_{0}^{\,3} {\sqrt{1+2^{2x} }}\,dx$
E. $\displaystyle \int_{0}^{\,3} {\sqrt{1+2^{x} }}\,dx$
F. $\displaystyle \int_{0}^{\,3} {\sqrt{1+(\ln2)^2 2^{x} }}\,dx$