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

The integral of sqrt(x)-1 is 2/3 x^{3/2}-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(x)-1

\int x - 1 d x

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

Solution steps

\int x - 1 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 x d x - \int 1 d x

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

\int 1 d x = x

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

Add a constant to the solution

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

y = (\frac{x - 1}{x + 1})

\frac{\partial}{\partial x} (x^{2} y + 2 x^{2} - y - 2)

x \to 0 + lim (f (x))

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

f (t) = 7 t + 3

What is the integral of sqrt(x)-1 ?
The integral of sqrt(x)-1 is 2/3 x^{3/2}-x+C