What is the integral from 0 to 5 of 5ln(x) ?

The integral from 0 to 5 of 5ln(x) is 5(5ln(5)-5)

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integral from 0 to 5 of 5ln(x)

\int_{0}^{5} 5 ln (x) d x

5 (5 ln (5) - 5)

Decimal Notation

15.23594 \dots

Solution steps

\int_{0}^{5} 5 ln (x) d x

Take the constant out:

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

= 5 \cdot \int_{0}^{5} ln (x) d x

Apply Integration By Parts

: [x ln (x) - \int 1 d x]_{0}^{5}

= 5 [x ln (x) - \int 1 d x]_{0}^{5}

\int 1 d x = x

= 5 [x ln (x) - x]_{0}^{5}

Compute the boundaries:

5 ln (5) - 5

= 5 (5 ln (5) - 5)

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What is the integral from 0 to 5 of 5ln(x) ?
The integral from 0 to 5 of 5ln(x) is 5(5ln(5)-5)