What is the integral from 4 to 6 of 1/(xln(1.5)) ?

The integral from 4 to 6 of 1/(xln(1.5)) is 1

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integral from 4 to 6 of 1/(xln(1.5))

\int_{4}^{6} \frac{1}{x ln ( 1.5 )} d x

1

Solution steps

\int_{4}^{6} \frac{1}{x ln ( 1.5 )} d x

Take the constant out:

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

= \frac{1}{ln ( 1.5 )} \cdot \int_{4}^{6} \frac{1}{x} d x

\frac{1}{ln ( 1.5 )} = 2.46630 \dots

= 2.46630 \dots \cdot \int_{4}^{6} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 2.46630 \dots [ln ∣ x ∣]_{4}^{6}

Compute the boundaries:

ln (6) - 2 ln (2)

= 2.46630 \dots (ln (6) - 2 ln (2))

Simplify

= 1

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What is the integral from 4 to 6 of 1/(xln(1.5)) ?
The integral from 4 to 6 of 1/(xln(1.5)) is 1