What is the integral of (12-x)/(sqrt(x)) ?

The integral of (12-x)/(sqrt(x)) is 24sqrt(x)-2/3 x^{3/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (12-x)/(sqrt(x))

\int \frac{12 - x}{x} d x

24 x - \frac{2}{3} x^{\frac{3}{2}} + C

Solution steps

\int \frac{12 - x}{x} d x

Expand

\frac{12 - x}{x} : \frac{12}{x} - x

= \int \frac{12}{x} - x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{12}{x} d x - \int x d x

\int \frac{12}{x} d x = 24 x

\int x d x = \frac{2}{3} x^{\frac{3}{2}}

= 24 x - \frac{2}{3} x^{\frac{3}{2}}

Add a constant to the solution

= 24 x - \frac{2}{3} x^{\frac{3}{2}} + C

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

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

\int \frac{4 x ^{3} - 7 x}{x} d x

\int x (2 x + 1)^{3} d x

\int (3 x^{2} - 2) d x

What is the integral of (12-x)/(sqrt(x)) ?
The integral of (12-x)/(sqrt(x)) is 24sqrt(x)-2/3 x^{3/2}+C