What is the integral from a to a+b of 1/x ?

The integral from a to a+b of 1/x is ln|a+b|-ln|a|

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integral from a to a+b of 1/x

\int_{a}^{a + b} \frac{1}{x} d x

ln ∣ a + b ∣ - ln ∣ a ∣

Solution steps

\int_{a}^{a + b} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= [ln ∣ x ∣]_{a}^{a + b}

Compute the boundaries:

ln ∣ a + b ∣ - ln ∣ a ∣

= ln ∣ a + b ∣ - ln ∣ a ∣

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What is the integral from a to a+b of 1/x ?
The integral from a to a+b of 1/x is ln|a+b|-ln|a|