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

The integral of 1/((2-x)sqrt(1-x)) is -2arctan(sqrt(1-x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/((2-x)sqrt(1-x))

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

- 2 arctan (1 - x) + C

Solution steps

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

Apply u-substitution

: \int - \frac{2}{u ^{2} + 1} d u

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

Use the common integral:

\int \frac{1}{u ^{2} + 1} d u = arctan (u)

= - 2 arctan (u)

Substitute back

u = 1 - x

= - 2 arctan (1 - x)

Add a constant to the solution

= - 2 arctan (1 - x) + C

\int (t + 7) e^{2 t + 3} d t

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

y^{2} - 7 x = 1, x - y = 1

\int 6 e^{5} d x

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

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