What is the integral of sqrt((x-6)/x) ?

The integral of sqrt((x-6)/x) is sqrt((x-6)/x)x-6ln| 1/(sqrt(6))sqrt(x-6)+sqrt(x/6)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sqrt((x-6)/x)

\int \frac{x - 6}{x} d x

\frac{x - 6}{x} x - 6 ln \frac{1}{6} x - 6 + \frac{x}{6} + C

Solution steps

\int \frac{x - 6}{x} d x

Apply Integration By Parts

: \frac{x - 6}{x} x - \int \frac{3}{x ^{\frac{1}{2}} x - 6} d x

= \frac{x - 6}{x} x - \int \frac{3}{x ^{\frac{1}{2}} x - 6} d x

\int \frac{3}{x ^{\frac{1}{2}} x - 6} d x = 6 ln \frac{1}{6} x - 6 + \frac{x}{6}

= \frac{x - 6}{x} x - 6 ln \frac{1}{6} x - 6 + \frac{x}{6}

Add a constant to the solution

= \frac{x - 6}{x} x - 6 ln \frac{1}{6} x - 6 + \frac{x}{6} + C

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

\int x e^{22 x} d x

\int \frac{r ^{2} + 1}{r - 3} d r

\int - cos (nπ x) d x

\int (x + 5) 6 - x d x

What is the integral of sqrt((x-6)/x) ?
The integral of sqrt((x-6)/x) is sqrt((x-6)/x)x-6ln| 1/(sqrt(6))sqrt(x-6)+sqrt(x/6)|+C