Phương pháp giải:

Sử dụng phương pháp vi phân.

Lời giải chi tiết:

Ta có: \(d\left( {2x} \right) = 2dx \Rightarrow dx = \dfrac{1}{2}d\left( {2x} \right)\).

\(\begin{array}{l} \Rightarrow \int {f\left( {2x} \right)dx}  = \int {f\left( {2x} \right)\dfrac{{d\left( {2x} \right)}}{2}} \\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \dfrac{1}{2}\int {f\left( {2x} \right)d\left( {2x} \right)} \\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \dfrac{1}{2}.\left[ {2.\left( {2x} \right).{e^{2.2x + 1}}} \right] + C\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 2x{e^{4x + 1}} + C\end{array}\)

Chọn B.