What is the integral from 0 to y of 1/(1-x) ?

The integral from 0 to y of 1/(1-x) is -ln|-y+1|

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integral from 0 to y of 1/(1-x)

\int_{0}^{y} \frac{1}{1 - x} d x

- ln ∣ - y + 1 ∣

Solution steps

\int_{0}^{y} \frac{1}{1 - x} d x

Apply u-substitution

: \int_{1}^{1 - y} - \frac{1}{u} d u

= \int_{1}^{1 - y} - \frac{1}{u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int_{1}^{1 - y} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - [ln ∣ u ∣]_{1}^{1 - y}

Compute the boundaries:

ln ∣ - y + 1 ∣

= - ln ∣ - y + 1 ∣

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What is the integral from 0 to y of 1/(1-x) ?
The integral from 0 to y of 1/(1-x) is -ln|-y+1|