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

The integral from 1 to e of ln(8x) is eln(8e)-e-3ln(2)+1

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integral from 1 to e of ln(8x)

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

e ln (8 e) - e - 3 ln (2) + 1

Decimal

4.57306 \dots

Solution steps

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

Apply Integration By Parts

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

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

\int 1 d x = x

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

Compute the boundaries:

e ln (8 e) - e - 3 ln (2) + 1

= e ln (8 e) - e - 3 ln (2) + 1

\frac{d}{d x} (\frac{1}{2 x - 3})

f (x) = \frac{3 x + 2}{x + 1}

\frac{1}{2} (6 t + 3)^{- \frac{1}{2}}

x^{2} - 7 x - 26, - x^{2} + 3 x + 2

y^{^{'}} = x (x - 1) (x - 5)

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