What is the integral from a to x of 1/x ?

The integral from a to x of 1/x is ln|x|-ln|a|

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integral from a to x of 1/x

\int_{a}^{x} \frac{1}{x} d x

ln ∣ x ∣ - ln ∣ a ∣

Solution steps

\int_{a}^{x} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= [ln ∣ x ∣]_{a}^{x}

Compute the boundaries:

ln ∣ x ∣ - ln ∣ a ∣

= ln ∣ x ∣ - ln ∣ a ∣

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

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

\int_{4}^{8} 8 x - x^{2} d x

\int_{e}^{e^{x}} \frac{cos ( ln ( x ) )}{x} d x

\int_{T}^{T^{^{'}}} 1 d T

What is the integral from a to x of 1/x ?
The integral from a to x of 1/x is ln|x|-ln|a|