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

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

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

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

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

Solution steps

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

Simplify

ln (e^{x}) : x

= \int x d x

Apply the Power Rule

: \frac{2}{3} x^{\frac{3}{2}}

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

Add a constant to the solution

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

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