What is the integral from 3 to 15 of 1/x ?

The integral from 3 to 15 of 1/x is ln(5)

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integral from 3 to 15 of 1/x

\int_{3}^{15} \frac{1}{x} d x

ln (5)

Decimal

1.60943 \dots

Solution steps

\int_{3}^{15} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= [ln ∣ x ∣]_{3}^{15}

Compute the boundaries:

ln (15) - ln (3)

= ln (15) - ln (3)

Simplify

= ln (5)

\int_{1}^{8} 1 + x d x

\int_{1}^{4} \frac{3}{x} d x

\int_{0}^{1} - (x - 1) d x

\int_{0}^{2 π} - 54 sin^{2} (θ) d θ

\int_{0}^{5} x + 5 d x

What is the integral from 3 to 15 of 1/x ?
The integral from 3 to 15 of 1/x is ln(5)