What is the integral of 1/(sqrt(x)(1-2\sqrt{x))} ?

The integral of 1/(sqrt(x)(1-2\sqrt{x))} is -ln|1-2sqrt(x)|+C

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integral of 1/(sqrt(x)(1-2\sqrt{x))}

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

- ln 1 - 2 x + C

Solution steps

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

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - ln ∣ u ∣

Substitute back

u = 1 - 2 x

= - ln 1 - 2 x

Add a constant to the solution

= - ln 1 - 2 x + C

y = \frac{7}{ln ( x )}

\frac{d}{d x} (\frac{5 x}{6})

x \to 9 - lim (\frac{1}{x - 9})

x \to 0 + lim (x [ln (x)]^{2})

\frac{d}{d x} (2^{5 x} 3^{4 x^{2}})

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