What is the integral from 1 to e^8 of 4/x ?

The integral from 1 to e^8 of 4/x is 32

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integral from 1 to e^8 of 4/x

\int_{1}^{e^{8}} \frac{4}{x} d x

32

Solution steps

\int_{1}^{e^{8}} \frac{4}{x} d x

Take the constant out:

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

= 4 \cdot \int_{1}^{e^{8}} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 4 [ln ∣ x ∣]_{1}^{e^{8}}

Compute the boundaries:

8

= 4 \cdot 8

Simplify

= 32

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What is the integral from 1 to e^8 of 4/x ?
The integral from 1 to e^8 of 4/x is 32