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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

- 2 ln ∣ 1 - y ∣ + C

Solution steps

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

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 - y

= - 2 ln ∣ 1 - y ∣

Add a constant to the solution

= - 2 ln ∣ 1 - y ∣ + C

\int \frac{1}{9 x ^{2} - 6 x + 7} d x

\int \frac{4}{4 + x ^{2}} d x

\int \frac{2 x}{( 1 - x ) ^{7}} d x

\int cot (8 x) d x

\int e^{\frac{1}{s e c ( 2 x )}} sin (2 x) d x

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