What is the integral of sqrt(8-3x) ?

The integral of sqrt(8-3x) is -2/9 (8-3x)^{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(8-3x)

\int 8 - 3 x d x

- \frac{2}{9} (8 - 3 x)^{\frac{3}{2}} + C

Solution steps

\int 8 - 3 x d x

Apply u-substitution

: \int - \frac{u}{3} d u

= \int - \frac{u}{3} d u

Take the constant out:

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

= - \frac{1}{3} \cdot \int u d u

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

= - \frac{1}{3} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 8 - 3 x

= - \frac{1}{3} \cdot \frac{2}{3} (8 - 3 x)^{\frac{3}{2}}

Simplify

- \frac{1}{3} \cdot \frac{2}{3} (8 - 3 x)^{\frac{3}{2}} : - \frac{2}{9} (8 - 3 x)^{\frac{3}{2}}

= - \frac{2}{9} (8 - 3 x)^{\frac{3}{2}}

Add a constant to the solution

= - \frac{2}{9} (8 - 3 x)^{\frac{3}{2}} + C

\int x^{2} e^{2 x^{3} + 4} d x

\int \frac{x}{x ^{2} + 10} d x

\int \frac{2}{( 2 x - 3 ) ln ( 2 x - 3 )} d x

\int - z e^{- yz} d y

\int 10.2 + 2.5 x + 0.1 x^{2} d x

What is the integral of sqrt(8-3x) ?
The integral of sqrt(8-3x) is -2/9 (8-3x)^{3/2}+C