What is the integral from 0 to e^9 of ln(8x) ?

The integral from 0 to e^9 of ln(8x) is 3e^9ln(2)+8e^9

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integral from 0 to e^9 of ln(8x)

\int_{0}^{e^{9}} ln (8 x) d x

3 e^{9} ln (2) + 8 e^{9}

Decimal

81674.56075 \dots

Solution steps

\int_{0}^{e^{9}} ln (8 x) d x

Apply Integration By Parts

= [x ln (8 x) - \int 1 d x]_{0}^{e^{9}}

\int 1 d x = x

= [x ln (8 x) - x]_{0}^{e^{9}}

Compute the boundaries:

3 e^{9} ln (2) + 8 e^{9}

= 3 e^{9} ln (2) + 8 e^{9}

What is the integral from 0 to e^9 of ln(8x) ?
The integral from 0 to e^9 of ln(8x) is 3e^9ln(2)+8e^9