What is the integral from 2 to 4 of 3ln(x) ?

The integral from 2 to 4 of 3ln(x) is 3(6ln(2)-2)

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integral from 2 to 4 of 3ln(x)

\int_{2}^{4} 3 ln (x) d x

3 (6 ln (2) - 2)

Decimal Notation

6.47664 \dots

Solution steps

\int_{2}^{4} 3 ln (x) d x

Take the constant out:

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

= 3 \cdot \int_{2}^{4} ln (x) d x

Apply Integration By Parts

: [x ln (x) - \int 1 d x]_{2}^{4}

= 3 [x ln (x) - \int 1 d x]_{2}^{4}

\int 1 d x = x

= 3 [x ln (x) - x]_{2}^{4}

Compute the boundaries:

6 ln (2) - 2

= 3 (6 ln (2) - 2)

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What is the integral from 2 to 4 of 3ln(x) ?
The integral from 2 to 4 of 3ln(x) is 3(6ln(2)-2)