Question

Evaluate:$\int \ln \left(\frac{1}{e^x}\right)dx$

Answer 1

$\int \ln \left(\frac{1}{e^x}\right)dx$

$=\int \ln \left(e^{-x}\right)dx$

$=\int -x\ln edx$

$=-\int xdx$

$=\frac{-x^2}{2}+c$ where $c$ is the constant of integration.