What is the integral of 1/(1-(x/L)) ?

The integral of 1/(1-(x/L)) is -Lln|1-x/L |+C

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integral of 1/(1-(x/L))

\int \frac{1}{1 - ( \frac{x}{L} )} d x

- L ln 1 - \frac{x}{L} + C

Solution steps

\int \frac{1}{1 - \frac{x}{L}} d x

Apply u-substitution

: \int - \frac{L}{u} d u

= \int - \frac{L}{u} d u

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - L ln ∣ u ∣

Substitute back

u = 1 - \frac{x}{L}

= - L ln 1 - \frac{x}{L}

Add a constant to the solution

= - L ln 1 - \frac{x}{L} + C

\frac{d y}{d x} + 2 y = 1

\frac{d y}{d x} + 3 x^{2} \cdot y = 6 x^{2}

\frac{\partial}{\partial y} (arctan (x y))

\frac{d}{d x} (2 sin^{3} (x))

y = x^{2} sin^{4} (x) + x cos^{- 2} (x)

What is the integral of 1/(1-(x/L)) ?
The integral of 1/(1-(x/L)) is -Lln|1-x/L |+C