What is the integral from 0 to 1 of ln(8x) ?

The integral from 0 to 1 of ln(8x) is 3ln(2)-1

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integral from 0 to 1 of ln(8x)

\int_{0}^{1} ln (8 x) d x

3 ln (2) - 1

Decimal Notation

1.07944 \dots

Solution steps

\int_{0}^{1} ln (8 x) d x

Apply Integration By Parts

: [x ln (8 x) - \int 1 d x]_{0}^{1}

= [x ln (8 x) - \int 1 d x]_{0}^{1}

\int 1 d x = x

= [x ln (8 x) - x]_{0}^{1}

Compute the boundaries:

3 ln (2) - 1

= 3 ln (2) - 1

\frac{d}{d x} (3 tan (2 x + 1) + x)

x \to - \infty lim (e^{5 x})

\int \frac{x + 1}{x ^{2} + 9} d x

\frac{d}{d x} (cot (x) tan (x))

\int sin (x) \cdot e^{3 x} d x

What is the integral from 0 to 1 of ln(8x) ?
The integral from 0 to 1 of ln(8x) is 3ln(2)-1