What is the integral from 1 to 8 of 3/t ?

The integral from 1 to 8 of 3/t is 9ln(2)

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integral from 1 to 8 of 3/t

\int_{1}^{8} \frac{3}{t} d t

9 ln (2)

Decimal

6.23832 \dots

Solution steps

\int_{1}^{8} \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}^{8} \frac{1}{t} d t

Use the common integral:

\int \frac{1}{t} d t = ln (∣ t ∣)

= 3 [ln ∣ t ∣]_{1}^{8}

Compute the boundaries:

3 ln (2)

= 3 \cdot 3 ln (2)

Simplify

= 9 ln (2)

\int_{- 3}^{3} x^{2} - x d x

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\int_{0}^{9} \frac{y ^{3}}{9} d y

\int_{0}^{9} \frac{x}{4 + 5 x} d x

\int_{0}^{5} (x - 2)^{3} d x

What is the integral from 1 to 8 of 3/t ?
The integral from 1 to 8 of 3/t is 9ln(2)