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

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

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

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

- 2 ln 1 - x + C

Solution steps

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

= - 2 ln 1 - x

Add a constant to the solution

= - 2 ln 1 - x + C

\int (x^{2} - x) e^{x} d x

y^{^{'}} = y (1 - y), y (0) = 12

\int \frac{1}{x ^{2} 3 x - 1} d x

\int 2 x (x^{2} + 3)^{4} d x

\frac{\partial}{\partial y} (y sin (x y))

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