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

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

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

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

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

Solution steps

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

Simplify

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

= \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= \frac{u ^{3}}{3}

Add a constant to the solution

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

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