Cho hàm số f(x) thỏa mãn f'(x)= (x+ 3)e^x (mọi x thuộc R) và

Đáp án B

Ta có: $f\left(x\right)=f\left(x+2\right)e^{x}dx$. Đặt $\left\{\begin{array}{l}u=x+3\\ dv=e^x\end{array}\right.\Rightarrow \left\{\begin{array}{l}du=dx\\ v=e^x\end{array}\right.$

Suy ra $f\left(x\right)=\left(x+3\right)e^x-\underset{}{\overset{}{\int }}{e}^{x}dx+C=\left(x+2\right)e^x+C$

Mặt khác $f\left(0\right)=2e^0+C=5\iff C=3\Rightarrow f\left(x\right)=\left(x+2\right)e^x+3$

$I=\underset{0}{\overset{3}{\int }}f\left(x\right)dx=\underset{0}{\overset{3}{\int }}\left(x+2\right)e^{x}dx+\underset{0}{\overset{3}{\int }}3dx=\left(x+1\right)e^x\left|\begin{array}{l}{}^3\\ {}_0\end{array}\right.+9=4e^3+8$