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

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{\mathrm{e}^{\mathrm{x}} \mathrm{dx}}{\mathrm{e}^{\mathrm{x}}+\mathrm{e}}∫ex+eexdx​ A) x+Cx+Cx+C B) xe+C\frac{x}{e}+Cex​+C C) eln⁡∣ex+e∣+Ce \ln \left|e^{x}+e\right|+Celn∣ex+e∣+C

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