The value of $\int\frac{e^x}{x+2}[1+(x+2)\ln(x+2)]dx$ is:

$\frac{e^x}{x+2}\log(x+2)+C$ $e^x(x+2)\log(x+2)+C$ $e^x\ln(x+2)+C$ None of these

$e^x\ln(x+2)+C$

$\int e^x(\frac{1}{x+2}+\ln(x+2))dx=e^x\ln(x+2)+C$