What is the integral from 1 to e^5 of 2/x ?

The integral from 1 to e^5 of 2/x is 10

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integral from 1 to e^5 of 2/x

\int_{1}^{e^{5}} \frac{2}{x} d x

10

Solution steps

\int_{1}^{e^{5}} \frac{2}{x} d x

Take the constant out:

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

= 2 \cdot \int_{1}^{e^{5}} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 2 [ln ∣ x ∣]_{1}^{e^{5}}

Compute the boundaries:

5

= 2 \cdot 5

Simplify

= 10

\int_{- 2}^{- 1} (4 x^{3} + \frac{2}{x ^{3}}) d x

\int_{0}^{4} \frac{1}{1 - x} d x

\int_{0}^{3} x^{2} - 6 x + 9 d x

\int_{0}^{1} 6 e^{3 x} d x

\int_{0}^{4} 6 - 2 x d x

What is the integral from 1 to e^5 of 2/x ?
The integral from 1 to e^5 of 2/x is 10