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

The integral from 1 to e^5 of 5/x is 25

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integral from 1 to e^5 of 5/x

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

25

Solution steps

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 5 [ln ∣ x ∣]_{1}^{e^{5}}

Compute the boundaries:

5

= 5 \cdot 5

Simplify

= 25

f (x) = 1 + 4 - x, at x = 2

x \to \infty lim ((x) 3)

cos (2 x), 0

\frac{\partial}{\partial t} (r cos (t) sin (s))

\frac{d}{d x} (x (x - 4)^{3})

What is the integral from 1 to e^5 of 5/x ?
The integral from 1 to e^5 of 5/x is 25