What is the integral from 1 to e^3 of 5/x ?

The integral from 1 to e^3 of 5/x is 15

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integral from 1 to e^3 of 5/x

\int_{1}^{e^{3}} \frac{5}{x} d x

15

Solution steps

\int_{1}^{e^{3}} \frac{5}{x} d x

Take the constant out:

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

= 5 \cdot \int_{1}^{e^{3}} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 5 [ln ∣ x ∣]_{1}^{e^{3}}

Compute the boundaries:

3

= 5 \cdot 3

Simplify

= 15

\int_{0}^{1} x^{5} \cdot e^{- x} d x

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What is the integral from 1 to e^3 of 5/x ?
The integral from 1 to e^3 of 5/x is 15