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

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

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integral from 1 to e of 2ln(x)

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

2

Solution steps

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

Take the constant out:

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

= 2 \cdot \int_{1}^{e} ln (x) d x

Apply Integration By Parts

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

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

\int 1 d x = x

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

Compute the boundaries:

1

= 2 \cdot 1

Simplify

= 2

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