What is the integral from 2 to 5 of ln(5x) ?

The integral from 2 to 5 of ln(5x) is ln(390625/4)-3

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integral from 2 to 5 of ln(5x)

\int_{2}^{5} ln (5 x) d x

ln (\frac{390625}{4}) - 3

Decimal

8.48920 \dots

Solution steps

\int_{2}^{5} ln (5 x) d x

Apply Integration By Parts

= [x ln (5 x) - \int 1 d x]_{2}^{5}

\int 1 d x = x

= [x ln (5 x) - x]_{2}^{5}

Compute the boundaries:

10 ln (5) - 3 - 2 ln (10)

= 10 ln (5) - 3 - 2 ln (10)

Simplify

= ln (\frac{390625}{4}) - 3

What is the integral from 2 to 5 of ln(5x) ?
The integral from 2 to 5 of ln(5x) is ln(390625/4)-3