Integral M Ex E5D3A4
1. **State the problem:** We need to evaluate the integral $$\int \frac{m}{1 e^x} \, dm$$.
2. **Analyze the integral:** The integral is with respect to $m$, and the integrand is $$\frac{m}{1 e^x} = \frac{m}{e^x}$$ since $1 e^x = e^x$.
3. **Treat $e^x$ as a constant:** Since the integration is with respect to $m$, and $x$ is independent of $m$, $e^x$ is a constant.
4. **Rewrite the integral:**
$$\int \frac{m}{e^x} \, dm = \frac{1}{e^x} \int m \, dm$$
5. **Integrate with respect to $m$:**
$$\int m \, dm = \frac{m^2}{2} + C$$
6. **Combine results:**
$$\frac{1}{e^x} \cdot \frac{m^2}{2} + C = \frac{m^2}{2 e^x} + C$$
**Final answer:**
$$\int \frac{m}{1 e^x} \, dm = \frac{m^2}{2 e^x} + C$$