What is the integral from 1 to 9 of 3/t ?

The integral from 1 to 9 of 3/t is 6ln(3)

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integral from 1 to 9 of 3/t

\int_{1}^{9} \frac{3}{t} d t

6 ln (3)

Decimal

6.59167 \dots

Solution steps

\int_{1}^{9} \frac{3}{t} d t

Take the constant out:

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

= 3 \cdot \int_{1}^{9} \frac{1}{t} d t

Use the common integral:

\int \frac{1}{t} d t = ln (∣ t ∣)

= 3 [ln ∣ t ∣]_{1}^{9}

Compute the boundaries:

2 ln (3)

= 3 \cdot 2 ln (3)

Simplify

= 6 ln (3)

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What is the integral from 1 to 9 of 3/t ?
The integral from 1 to 9 of 3/t is 6ln(3)