24 multiple choice 1 point ∫(e^x / (1 + e^x)) dx = (a) ln((1 / e^x)+1)+c (b) ln(1 + e^x)+c (c) x - ln(1 +…

Answer:

B. $\ln(1 + e^{x})+C$

Explanation:

Step1: Use substitution

Let $u = 1 + e^{x}$, then $du=e^{x}dx$.

Step2: Rewrite the integral

The integral $\int\frac{e^{x}}{1 + e^{x}}dx$ becomes $\int\frac{du}{u}$.

Step3: Integrate

We know that $\int\frac{du}{u}=\ln|u|+C$.

Step4: Substitute back

Substituting $u = 1 + e^{x}$ back, we get $\ln(1 + e^{x})+C$.