## Related questions with answers

Question

Evaluate the integrals. Assume a, b, A, B, $P_{0}$, h, and k are constants. $\int \frac{e^{x}}{2+e^{x}} d x$

Solution

VerifiedStep 1

1 of 2$\begin{align*} \int \frac{e^x}{2+e^x} \, \text{d}x &= \int \frac{1}{u} \, \text{d}u & & \color{#5a140a} \begin{gathered} \text{Substitute }\\ u=2+e^x \Rightarrow \text{d}u = e^x \; \text{d} x \end{gathered} \\[4pt] & = \ln \left| u \right| + C \\[4pt] & = \ln \left| 2+e^x \right| + C & & \color{#5a140a} {u=2+e^x } \\[4pt] & = \ln \left( 2+e^x \right) +C & & \color{#5a140a} {2+e^x>0 } \end{align*}$

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