en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of 9x^{1/2}

Solution

\int 9 x^{\frac{1}{2}} d x

Solution

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

Solution steps

\int 9 x^{\frac{1}{2}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 9 \cdot \int x^{\frac{1}{2}} d x

Apply the Power Rule

= 9 \cdot \frac{2}{3} x^{\frac{3}{2}}

Simplify

9 \cdot \frac{2}{3} x^{\frac{3}{2}} : 6 x^{\frac{3}{2}}

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

Add a constant to the solution

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

Graph

Popular Examples

limit as x approaches infinity of 2x-3

x \to \infty lim (2 x - 3)

taylor 5/(sqrt(x)),4

t a y l or \frac{5}{x}, 4

sum from n=0 to infinity of 1/(e^{5n)}

n = 0 \sum \infty \frac{1}{e ^{5 n}}

integral of (-4x^3+2e^{-2x}+1/(2x))

\int (- 4 x^{3} + 2 e^{- 2 x} + \frac{1}{2 x}) d x

(dy)/(dx)+4(tan(4x))y=10cos(4x)

\frac{d y}{d x} + 4 (tan (4 x)) y = 10 cos (4 x)

Frequently Asked Questions (FAQ)

What is the integral of 9x^{1/2} ?
The integral of 9x^{1/2} is 6x^{3/2}+C