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

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

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integral of 1/((1-2x))

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

- \frac{1}{2} ln ∣ 1 - 2 x ∣ + C

Solution steps

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

Apply u-substitution

: \int - \frac{1}{2 u} d u

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - \frac{1}{2} ln ∣ u ∣

Substitute back

u = 1 - 2 x

= - \frac{1}{2} ln ∣ 1 - 2 x ∣

Add a constant to the solution

= - \frac{1}{2} ln ∣ 1 - 2 x ∣ + C

x \to 2 π - lim (x csc (x))

\frac{d}{d x} (5 x^{2} + 4)

x \to - 5 lim (∣ x + 5 ∣)

\frac{\partial}{\partial x} (x^{\frac{1}{2}} y)

\frac{d y}{d x} = 3 + 2 - 5 y

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