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

The integral of 2/(sqrt(x)\sqrt{1-x)} is 4arcsin(sqrt(x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

4 arcsin (x) + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{1 - u ^{2}} d u = arcsin (u)

= 2 \cdot 2 arcsin (u)

Substitute back

u = x

= 2 \cdot 2 arcsin (x)

Simplify

= 4 arcsin (x)

Add a constant to the solution

= 4 arcsin (x) + C

What is the integral of 2/(sqrt(x)\sqrt{1-x)} ?
The integral of 2/(sqrt(x)\sqrt{1-x)} is 4arcsin(sqrt(x))+C