What is the integral from 4 to 5 of 1/(5x-1) ?

The integral from 4 to 5 of 1/(5x-1) is 1/5 (ln(24)-ln(19))

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integral from 4 to 5 of 1/(5x-1)

\int_{4}^{5} \frac{1}{5 x - 1} d x

\frac{1}{5} (ln (24) - ln (19))

Decimal Notation

0.04672 \dots

Solution steps

\int_{4}^{5} \frac{1}{5 x - 1} d x

Apply u-substitution

: \int_{19}^{24} \frac{1}{5 u} d u

= \int_{19}^{24} \frac{1}{5 u} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int_{19}^{24} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{5} [ln ∣ u ∣]_{19}^{24}

Compute the boundaries:

ln (24) - ln (19)

= \frac{1}{5} (ln (24) - ln (19))

x y^{^{'}} + 3 y = \frac{4 e ^{2 x}}{x ^{2}}

x \to 1 lim (\frac{2 x}{x - 1})

f (x) = 9 x^{5} (x^{3} - 2 x)

y^{^{''}} - 2 y^{^{'}} - 63 y = 0

n = 1 \sum \infty \frac{1}{n ^{- 1}}

What is the integral from 4 to 5 of 1/(5x-1) ?
The integral from 4 to 5 of 1/(5x-1) is 1/5 (ln(24)-ln(19))