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

The integral from 1 to 5e of 1/(3x) is 1/3 ln(5e)

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integral from 1 to 5e of 1/(3x)

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

\frac{1}{3} ln (5 e)

Decimal Notation

0.86981 \dots

Solution steps

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{1}{3} [ln ∣ x ∣]_{1}^{5 e}

Compute the boundaries:

ln (5 e)

= \frac{1}{3} ln (5 e)

\int \frac{5 ln ( x )}{x} d x

\int (2 - 3 x)^{5} d x

n = 5 \sum \infty sin^{2} (n)

\int 4 sin (3 t) + 1.2 e^{- 6 t} d t

y = \frac{2}{x}, (- 4, - \frac{1}{2})

What is the integral from 1 to 5e of 1/(3x) ?
The integral from 1 to 5e of 1/(3x) is 1/3 ln(5e)