What is the integral of (100)/(100-y) ?

The integral of (100)/(100-y) is -100ln|100-y|+C

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integral of (100)/(100-y)

\int \frac{100}{100 - y} d y

- 100 ln ∣ 100 - y ∣ + C

Solution steps

\int \frac{100}{100 - y} d y

Take the constant out:

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

= 100 \cdot \int \frac{1}{100 - y} d y

Apply u-substitution

= 100 \cdot \int - \frac{1}{u} d u

Take the constant out:

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

= 100 (- \int \frac{1}{u} d u)

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 100 (- ln ∣ u ∣)

Substitute back

u = 100 - y

= 100 (- ln ∣ 100 - y ∣)

Simplify

= - 100 ln ∣ 100 - y ∣

Add a constant to the solution

= - 100 ln ∣ 100 - y ∣ + C

What is the integral of (100)/(100-y) ?
The integral of (100)/(100-y) is -100ln|100-y|+C