What is the integral from 1 to ln(x) of 1/t ?

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

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integral from 1 to ln(x) of 1/t

\int_{1}^{l n (x)} \frac{1}{t} d t

ln ∣ ln (x) ∣

Solution steps

\int_{1}^{l n (x)} \frac{1}{t} d t

Use the common integral:

\int \frac{1}{t} d t = ln (∣ t ∣)

= [ln ∣ t ∣]_{1}^{l n (x)}

Compute the boundaries:

ln ∣ ln (x) ∣

= ln ∣ ln (x) ∣

\int \frac{1}{x ^{\frac{2}{3}}} d x

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

y = \frac{x ^{2}}{x + 3}, (2, \frac{4}{5})

f (x) = 4 x^{2} + 1

y^{^{'}} + \frac{1}{2} y = 8, y (0) = 2

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