What is the integral from 0 to 1 of 2/(3x) ?

The integral from 0 to 1 of 2/(3x) is diverges

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integral from 0 to 1 of 2/(3x)

\int_{0}^{1} \frac{2}{3 x} d x

diverges

Solution steps

\int_{0}^{1} \frac{2}{3 x} d x

Take the constant out:

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

= \frac{2}{3} \cdot \int_{0}^{1} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{2}{3} [ln ∣ x ∣]_{0}^{1}

Compute the boundaries:

diverges

= diverges

\int_{1}^{2} x^{2} - 4 d x

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\int_{- 2}^{2} e^{- x} d x

\int_{1}^{1} 1 - z d z

What is the integral from 0 to 1 of 2/(3x) ?
The integral from 0 to 1 of 2/(3x) is diverges