Question

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Explanation:

Step1: Expand the integrand

$$\int e^{-u}(e^{2u}+e^{u})du=\int(e^{u} + 1)du$$

Step2: Integrate term - by - term

$$\int(e^{u}+1)du=\int e^{u}du+\int 1du$$
Since $\int e^{u}du = e^{u}+C_1$ and $\int 1du=u + C_2$

Answer:

$e^{u}+u + C$ ($C = C_1 + C_2$ is the constant of integration)