What is the integral from a to 9a of 1/x ?

The integral from a to 9a of 1/x is 2ln(3)

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integral from a to 9a of 1/x

\int_{a}^{9 a} \frac{1}{x} d x

2 ln (3)

Decimal Notation

2.19722 \dots

Solution steps

\int_{a}^{9 a} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= [ln ∣ x ∣]_{a}^{9 a}

Compute the boundaries:

ln (9 ∣ a ∣) - ln ∣ a ∣

= ln (9 ∣ a ∣) - ln ∣ a ∣

Simplify

= 2 ln (3)

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\int_{0}^{x} 6 + 7 t^{2} d t

\int_{0}^{x} ∣ x ∣ d x

What is the integral from a to 9a of 1/x ?
The integral from a to 9a of 1/x is 2ln(3)