What is the integral of ln(sqrt(2x)) ?

The integral of ln(sqrt(2x)) is 1/2 xln(2x)-1/2 x+C

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integral of ln(sqrt(2x))

\int ln (2 x) d x

\frac{1}{2} x ln (2 x) - \frac{1}{2} x + C

Solution steps

\int ln (2 x) d x

Apply Integration By Parts

: x ln (2 x) - \int \frac{1}{2} d x

= x ln (2 x) - \int \frac{1}{2} d x

\int \frac{1}{2} d x = \frac{1}{2} x

= x ln (2 x) - \frac{1}{2} x

Simplify

ln (2 x) : \frac{1}{2} ln (2 x)

= \frac{1}{2} x ln (2 x) - \frac{1}{2} x

Add a constant to the solution

= \frac{1}{2} x ln (2 x) - \frac{1}{2} x + C

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