Find the integral.
-$\int \frac{e^{x} d x}{e^{x}+e}$
A) $\frac{x}{e}+C$
B) $\ln \left|e^{x}+e\right|+C$
C) $x+C$
D) $e \ln \left|e^{x}+e\right|+C$

Name: Find the integral. -$\int \frac{e^{x} d x}{e^{x}+e}$ A) $\frac{x}{e}+C$ B) $\ln \left|e^{x}+e\right|+C$ C) $x+C$ D) $e \ln \left|e^{x}+e\right|+C$
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Question

Quizplus · Accepted Answer

The integral can be solved using substitution. Let $ u = e^x + e $, then $ du = e^x dx $. The integral becomes $\int \frac{1}{u} du$, which is $\ln |u| + C$. Substituting back, we get $\ln |e^x + e| + C$.

Find the Integral ∫exdxex+e\int \frac{e^{x} d x}{e^{x}+e}∫ex+eexdx​ A) xe+C\frac{x}{e}+Cex​+C B) ln⁡∣ex+e∣+C\ln \left|e^{x}+e\right|+Cln∣ex+e∣+C C) x+Cx+Cx+C

Find the Integral $\int \frac{e^{x} d x}{e^{x}+e}$ A) $\frac{x}{e}+C$ B) $\ln \left|e^{x}+e\right|+C$ C) $x+C$