What is the integral from 5 to 6 of 1/(6x-1) ?

The integral from 5 to 6 of 1/(6x-1) is 1/6 (ln(35)-ln(29))

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integral from 5 to 6 of 1/(6x-1)

\int_{5}^{6} \frac{1}{6 x - 1} d x

\frac{1}{6} (ln (35) - ln (29))

Decimal Notation

0.03134 \dots

Solution steps

\int_{5}^{6} \frac{1}{6 x - 1} d x

Apply u-substitution

: \int_{29}^{35} \frac{1}{6 u} d u

= \int_{29}^{35} \frac{1}{6 u} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int_{29}^{35} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{6} [ln ∣ u ∣]_{29}^{35}

Compute the boundaries:

ln (35) - ln (29)

= \frac{1}{6} (ln (35) - ln (29))

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What is the integral from 5 to 6 of 1/(6x-1) ?
The integral from 5 to 6 of 1/(6x-1) is 1/6 (ln(35)-ln(29))