What is the integral from 6 to 10 of ((36)/x) ?

The integral from 6 to 10 of ((36)/x) is 36ln(5/3)

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integral from 6 to 10 of ((36)/x)

\int_{6}^{10} (\frac{36}{x}) d x

36 ln (\frac{5}{3})

Decimal Notation

18.38972 \dots

Solution steps

\int_{6}^{10} \frac{36}{x} d x

Take the constant out:

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

= 36 \cdot \int_{6}^{10} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 36 [ln ∣ x ∣]_{6}^{10}

Compute the boundaries:

ln (10) - ln (6)

= 36 (ln (10) - ln (6))

Simplify

= 36 ln (\frac{5}{3})

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What is the integral from 6 to 10 of ((36)/x) ?
The integral from 6 to 10 of ((36)/x) is 36ln(5/3)