What is the integral of (2-3x)^{3/2} ?

The integral of (2-3x)^{3/2} is -2/15 (2-3x)^{5/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2-3x)^{3/2}

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

- \frac{2}{15} (2 - 3 x)^{\frac{5}{2}} + C

Solution steps

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

Apply u-substitution

: \int - \frac{u ^{\frac{3}{2}}}{3} d u

= \int - \frac{u ^{\frac{3}{2}}}{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^{\frac{3}{2}} d u

Apply the Power Rule

: \frac{2}{5} u^{\frac{5}{2}}

= - \frac{1}{3} \cdot \frac{2}{5} u^{\frac{5}{2}}

Substitute back

u = 2 - 3 x

= - \frac{1}{3} \cdot \frac{2}{5} (2 - 3 x)^{\frac{5}{2}}

Simplify

- \frac{1}{3} \cdot \frac{2}{5} (2 - 3 x)^{\frac{5}{2}} : - \frac{2}{15} (2 - 3 x)^{\frac{5}{2}}

= - \frac{2}{15} (2 - 3 x)^{\frac{5}{2}}

Add a constant to the solution

= - \frac{2}{15} (2 - 3 x)^{\frac{5}{2}} + C

\int \frac{15}{64} + \frac{x}{64} d x

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

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

\int (3 + 7 x^{2})^{9} 5 x d x

\int (7 x^{2} + 1) d x

What is the integral of (2-3x)^{3/2} ?
The integral of (2-3x)^{3/2} is -2/15 (2-3x)^{5/2}+C