What is the integral of ln(e^{-x^2}) ?

The integral of ln(e^{-x^2}) is -x^3+(2x^3)/3+C

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integral of ln(e^{-x^2})

\int ln (e^{- x^{2}}) d x

- x^{3} + \frac{2 x ^{3}}{3} + C

Solution steps

\int ln (e^{- x^{2}}) d x

Apply Integration By Parts

= - x^{3} - \int - 2 x^{2} d x

\int - 2 x^{2} d x = - \frac{2 x ^{3}}{3}

= - x^{3} - (- \frac{2 x ^{3}}{3})

Simplify

= - x^{3} + \frac{2 x ^{3}}{3}

Add a constant to the solution

= - x^{3} + \frac{2 x ^{3}}{3} + C

What is the integral of ln(e^{-x^2}) ?
The integral of ln(e^{-x^2}) is -x^3+(2x^3)/3+C