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

The integral from 1 to n of 1/x is ln|n|

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integral from 1 to n of 1/x

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

ln ∣ n ∣

Solution steps

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= [ln ∣ x ∣]_{1}^{n}

Compute the boundaries:

ln ∣ n ∣

= ln ∣ n ∣

\int_{- 3}^{0} 1 - x d x

\int_{0}^{4} - x d x

\int_{- 7}^{2} \frac{1}{( x - 1 ) ^{\frac{5}{3}}} d x

\int_{- 2}^{3} x^{- 3} d x

\int_{0}^{2 π} \frac{1 - cos ( 2 x )}{2} d x

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