What is the integral from e to 4e of 1/x ?

The integral from e to 4e of 1/x is ln(4e)-1

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integral from e to 4e of 1/x

\int_{e}^{4 e} \frac{1}{x} d x

ln (4 e) - 1

Decimal Notation

1.38629 \dots

Solution steps

\int_{e}^{4 e} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= [ln ∣ x ∣]_{e}^{4 e}

Compute the boundaries:

ln (4 e) - 1

= ln (4 e) - 1

\int_{0}^{l n (3)} e^{x} - e^{- 4 x} d x

\frac{\partial}{\partial y} (1 + y^{2} sin (2 x))

\int x (1 + x^{2}) d x

\frac{d}{d x} (x^{3} - 12 x^{2} + 45 x)

What is the integral from e to 4e of 1/x ?
The integral from e to 4e of 1/x is ln(4e)-1