What is the integral from 1 to 5 of 2/t ?

The integral from 1 to 5 of 2/t is 2ln(5)

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integral from 1 to 5 of 2/t

\int_{1}^{5} \frac{2}{t} d t

2 ln (5)

Decimal

3.21887 \dots

Solution steps

\int_{1}^{5} \frac{2}{t} d t

Take the constant out:

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

= 2 \cdot \int_{1}^{5} \frac{1}{t} d t

Use the common integral:

\int \frac{1}{t} d t = ln (∣ t ∣)

= 2 [ln ∣ t ∣]_{1}^{5}

Compute the boundaries:

ln (5)

= 2 ln (5)

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What is the integral from 1 to 5 of 2/t ?
The integral from 1 to 5 of 2/t is 2ln(5)