What is the integral from 0 to 2 of 1/(7x+10) ?

The integral from 0 to 2 of 1/(7x+10) is 1/7 ln(12/5)

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integral from 0 to 2 of 1/(7x+10)

\int_{0}^{2} \frac{1}{7 x + 10} d x

\frac{1}{7} ln (\frac{12}{5})

Decimal Notation

0.12506 \dots

Solution steps

\int_{0}^{2} \frac{1}{7 x + 10} d x

Apply u-substitution

: \int_{10}^{24} \frac{1}{7 u} d u

= \int_{10}^{24} \frac{1}{7 u} d u

Take the constant out:

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

= \frac{1}{7} \cdot \int_{10}^{24} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{7} [ln ∣ u ∣]_{10}^{24}

Compute the boundaries:

ln (24) - ln (10)

= \frac{1}{7} (ln (24) - ln (10))

Simplify

= \frac{1}{7} ln (\frac{12}{5})

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What is the integral from 0 to 2 of 1/(7x+10) ?
The integral from 0 to 2 of 1/(7x+10) is 1/7 ln(12/5)