What is the integral of 1/(1-x/2) ?

The integral of 1/(1-x/2) is -2ln|1-x/2 |+C

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integral of 1/(1-x/2)

\int \frac{1}{1 - \frac{x}{2}} d x

- 2 ln 1 - \frac{x}{2} + C

Solution steps

\int \frac{1}{1 - \frac{x}{2}} d x

Apply u-substitution

: \int - \frac{2}{u} d u

= \int - \frac{2}{u} d u

Take the constant out:

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

= - 2 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - 2 ln ∣ u ∣

Substitute back

u = 1 - \frac{x}{2}

= - 2 ln 1 - \frac{x}{2}

Add a constant to the solution

= - 2 ln 1 - \frac{x}{2} + C

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