What is the integral from 1 to y of 1/y ?

The integral from 1 to y of 1/y is ln|y|

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integral from 1 to y of 1/y

\int_{1}^{y} \frac{1}{y} d y

ln ∣ y ∣

Solution steps

\int_{1}^{y} \frac{1}{y} d y

Use the common integral:

\int \frac{1}{y} d y = ln (∣ y ∣)

= [ln ∣ y ∣]_{1}^{y}

Compute the boundaries:

ln ∣ y ∣

= ln ∣ y ∣

\int_{0}^{1} \frac{2 x ^{2}}{x ^{2} + 1} d x

\int_{1}^{3} 95 + 432 t^{2} - 12 t d t

\int_{1}^{\infty} \frac{8}{x ^{2}} d x

\int_{x}^{2 x} \frac{1}{1 + t ^{4}} d t

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

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