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

The integral from 1 to e of (8ln(x)) is 8

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integral from 1 to e of (8ln(x))

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

8

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply Integration By Parts

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

\int 1 d x = x

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

Compute the boundaries:

1

= 8 \cdot 1

Simplify

= 8

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