What is the integral of x^{1/2}+6 ?

The integral of x^{1/2}+6 is 2/3 x^{3/2}+6x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^{1/2}+6

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

\frac{2}{3} x^{\frac{3}{2}} + 6 x + C

Solution steps

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

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

\int 6 d x = 6 x

= \frac{2}{3} x^{\frac{3}{2}} + 6 x

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} + 6 x + C

\int_{0}^{2} x^{3} (2 - x)^{2} d x

x \to 0 lim (\frac{e ^{x}}{ln ( x )})

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

17 - x^{2}

\frac{d y}{d x} \cdot x^{2} + x y = 1

What is the integral of x^{1/2}+6 ?
The integral of x^{1/2}+6 is 2/3 x^{3/2}+6x+C