What is the integral from 0 to 1 of ln(2x) ?

The integral from 0 to 1 of ln(2x) is ln(2)-1

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integral from 0 to 1 of ln(2x)

\int_{0}^{1} ln (2 x) d x

ln (2) - 1

Decimal

- 0.30685 \dots

Solution steps

\int_{0}^{1} ln (2 x) d x

Apply Integration By Parts

: [x ln (2 x) - \int 1 d x]_{0}^{1}

= [x ln (2 x) - \int 1 d x]_{0}^{1}

\int 1 d x = x

= [x ln (2 x) - x]_{0}^{1}

Compute the boundaries:

ln (2) - 1

= ln (2) - 1

\int (\frac{2}{x ^{2}}) d x

\frac{\partial}{\partial x} (\frac{1}{x} - \frac{y}{x})

\int tan^{2} (x) tan (x) d x

\int \frac{7}{( x - 3 ) x ^{2} - 6 x + 5} d x

\frac{\partial}{\partial x} (e^{- x} sin (x))

What is the integral from 0 to 1 of ln(2x) ?
The integral from 0 to 1 of ln(2x) is ln(2)-1