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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{2 - x}{x} x + 2 arcsin (\frac{1}{2} x) + C

Solution steps

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

Apply Integration By Parts

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

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

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

= \frac{2 - x}{x} x - (- 2 arcsin (\frac{1}{2} x))

Simplify

= \frac{2 - x}{x} x + 2 arcsin (\frac{1}{2} x)

Add a constant to the solution

= \frac{2 - x}{x} x + 2 arcsin (\frac{1}{2} x) + C

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

\int 9 - ∣ x ∣ d x

\int (2^{0} - 3^{0})^{π} d x

\int (x^{\frac{3}{2}} + 8)^{7} x d x

\int x sin (1 - 3 x) d x

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