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))

integral

\frac{1}{( 1 - 2 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

\frac{( x - 1 )}{( x ^{2} + x + 1 )}

\frac{( 1 + x ) ^{2}}{x ( 1 + x ^{2} )}

\frac{x ^{2} + x + 1}{x ( 1 - x )}

sin (2 x + 3) + cos (3 x - 2)

sin^{2} (5 x)

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