What is the integral from 5 to x of 1/t ?

The integral from 5 to x of 1/t is ln|x|-ln(5)

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integral from 5 to x of 1/t

\int_{5}^{x} \frac{1}{t} d t

ln ∣ x ∣ - ln (5)

Solution steps

\int_{5}^{x} \frac{1}{t} d t

Use the common integral:

\int \frac{1}{t} d t = ln (∣ t ∣)

= [ln ∣ t ∣]_{5}^{x}

Compute the boundaries:

ln ∣ x ∣ - ln (5)

= ln ∣ x ∣ - ln (5)

\int_{0}^{π} 2 x sin (2 x) d x

\int_{0}^{5} 1 - - x^{2} + 5 x - 4 d x

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

\int_{2}^{e} \frac{x ^{4} - 5 x}{x ^{2}} d x

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

What is the integral from 5 to x of 1/t ?
The integral from 5 to x of 1/t is ln|x|-ln(5)