What is the integral from 0 to 1 of (2ln(x)) ?

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

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integral from 0 to 1 of (2ln(x))

\int_{0}^{1} (2 ln (x)) d x

- 2

Solution steps

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

Apply Integration By Parts

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

= 2 [x ln (x) - \int 1 d x]_{0}^{1}

\int 1 d x = x

= 2 [x ln (x) - x]_{0}^{1}

Compute the boundaries:

- 1

= 2 (- 1)

Simplify

= - 2

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