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

The integral of sqrt(1)+sqrt(x) is 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 sqrt(1)+sqrt(x)

\int 1 + x d x

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

Solution steps

\int 1 + x d x

Simplify

= \int 1 + 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 1 d x + \int x d x

\int 1 d x = x

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

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

Add a constant to the solution

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

x \to 8 lim (\frac{x}{x ^{2} - 64})

x \frac{d y}{d x} + y^{2} + y = 0

\frac{d}{d x} (9 x + x^{2})

\int \frac{sin ( 5 x )}{e ^{c o s (5 x) - 1}} d x

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

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