What is the integral of 1/(4-0.9y) ?

The integral of 1/(4-0.9y) is -1.11111…ln|4-0.9y|+C

integral of 1/(4-0.9y)

\int \frac{1}{4 - 0.9 y} d y

- 1.11111 \dots ln ∣ 4 - 0.9 y ∣ + C

Solution steps

\int \frac{1}{4 - 0.9 y} d y

Apply u-substitution

= \int - \frac{1}{0.9 u} d u

Take the constant out:

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

= - \frac{1}{0.9} \cdot \int \frac{1}{u} d u

Simplify

= - 1.11111 \dots \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - 1.11111 \dots ln ∣ u ∣

Substitute back

u = 4 - 0.9 y

= - 1.11111 \dots ln ∣ 4 - 0.9 y ∣

Add a constant to the solution

= - 1.11111 \dots ln ∣ 4 - 0.9 y ∣ + C

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What is the integral of 1/(4-0.9y) ?
The integral of 1/(4-0.9y) is -1.11111…ln|4-0.9y|+C