Cho hàm số \(f\left( x \right)={{2}^{x}}+x+1\). Tìm \(\int{f\left( x \right)\text{d}x}\)

A. \(\int {f\left( x \right){\rm{d}}x}  = {2^x} + {x^2} + x + C\)

B. \(\int {f\left( x \right){\rm{d}}x}  = \frac{1}{{\ln 2}}{2^x} + \frac{1}{2}{x^2} + x + C\)

C. \(\int {f\left( x \right){\rm{d}}x}  = {2^x} + \frac{1}{2}{x^2} + x + C\)

D. \(\int {f\left( x \right){\rm{d}}x}  = \frac{1}{{x + 1}}{2^x} + \frac{1}{2}{x^2} + x + C\)