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

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

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

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

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

Solution steps

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

Simplify

ln (e^{x^{2}}) : x^{2}

= \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

= \frac{x ^{3}}{3}

Add a constant to the solution

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

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