What is the integral of 1/(1-0.5x) ?

The integral of 1/(1-0.5x) is -2ln|1-0.5x|+C

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integral of 1/(1-0.5x)

\int \frac{1}{1 - 0.5 x} d x

- 2 ln ∣ 1 - 0.5 x ∣ + C

Solution steps

\int \frac{1}{1 - 0.5 x} d x

Apply u-substitution

: \int - \frac{1}{0.5 u} d u

= \int - \frac{1}{0.5 u} d u

Take the constant out:

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

= - \frac{1}{0.5} \cdot \int \frac{1}{u} d u

Simplify

= - 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 - 0.5 x

= - 2 ln ∣ 1 - 0.5 x ∣

Add a constant to the solution

= - 2 ln ∣ 1 - 0.5 x ∣ + C

x \to 10 - lim (8 - x)

\frac{\partial}{\partial z} (x e^{z} + x y + z^{3} - 4)

\int e^{x} 1 - e^{2 x} d x

e^{1 - x}

x \frac{d y}{d x} + y + y^{2} = 0

What is the integral of 1/(1-0.5x) ?
The integral of 1/(1-0.5x) is -2ln|1-0.5x|+C