What is the integral of ln(1/(e^x)) ?

The integral of ln(1/(e^x)) is -x^2+(x^2)/2+C

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integral of ln(1/(e^x))

\int ln (\frac{1}{e ^{x}}) d x

- x^{2} + \frac{x ^{2}}{2} + C

Solution steps

\int ln (\frac{1}{e ^{x}}) d x

Apply Integration By Parts

: - x^{2} - \int - x d x

= - x^{2} - \int - x d x

\int - x d x = - \frac{x ^{2}}{2}

= - x^{2} - (- \frac{x ^{2}}{2})

Simplify

= - x^{2} + \frac{x ^{2}}{2}

Add a constant to the solution

= - x^{2} + \frac{x ^{2}}{2} + C

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What is the integral of ln(1/(e^x)) ?
The integral of ln(1/(e^x)) is -x^2+(x^2)/2+C