What is the integral from 1/2 to e/2 of ln(2x) ?

The integral from 1/2 to e/2 of ln(2x) is 1/2

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integral from 1/2 to e/2 of ln(2x)

\int_{\frac{1}{2}}^{\frac{e}{2}} ln (2 x) d x

\frac{1}{2}

Decimal

0.5

Solution steps

\int_{\frac{1}{2}}^{\frac{e}{2}} ln (2 x) d x

Apply Integration By Parts

= [x ln (2 x) - \int 1 d x]_{\frac{1}{2}}^{\frac{e}{2}}

\int 1 d x = x

= [x ln (2 x) - x]_{\frac{1}{2}}^{\frac{e}{2}}

Compute the boundaries:

\frac{1}{2}

= \frac{1}{2}

What is the integral from 1/2 to e/2 of ln(2x) ?
The integral from 1/2 to e/2 of ln(2x) is 1/2