What is the integral from 1 to e^3 of 2/x ?

The integral from 1 to e^3 of 2/x is 6

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integral from 1 to e^3 of 2/x

\int_{1}^{e^{3}} \frac{2}{x} d x

6

Solution steps

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 2 [ln ∣ x ∣]_{1}^{e^{3}}

Compute the boundaries:

3

= 2 \cdot 3

Simplify

= 6

\int_{0}^{x^{3}} e^{x^{2}} d x

\int_{- 2}^{4} (x) d x

\int_{0}^{\infty} x e^{- y x} d x

\int_{- \infty}^{- 4} \frac{7}{x ^{3}} d x

\int_{0}^{1} x 99 x^{2} + 1 d x

What is the integral from 1 to e^3 of 2/x ?
The integral from 1 to e^3 of 2/x is 6