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

x \to 1 lim (a x^{2} + b x + 1)

n = 0 \sum \infty \frac{2}{n ( n + 1 )}

x \to 0 lim (+ (\frac{1}{3} + \frac{5}{3 x}))

f (x) = - 2 t^{2} + 3 t - 6

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

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