What is the integral from 2 to 6 of 8/x ?

The integral from 2 to 6 of 8/x is 8ln(3)

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integral from 2 to 6 of 8/x

\int_{2}^{6} \frac{8}{x} d x

8 ln (3)

Decimal

8.78889 \dots

Solution steps

\int_{2}^{6} \frac{8}{x} d x

Take the constant out:

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

= 8 \cdot \int_{2}^{6} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 8 [ln ∣ x ∣]_{2}^{6}

Compute the boundaries:

ln (6) - ln (2)

= 8 (ln (6) - ln (2))

Simplify

= 8 ln (3)

\int_{- 1}^{4} x^{4} d x

\int_{0}^{2} 4 - t^{2} d t

\int_{0}^{1} x^{2} + 3 x d x

\int_{1}^{2} 4 x^{5} d x

\int_{- 1}^{1} x x^{2} + 4 d x

What is the integral from 2 to 6 of 8/x ?
The integral from 2 to 6 of 8/x is 8ln(3)