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

The integral of (2x)^{3/2} is (4*2^{1/2})/5 x^{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 (2x)^{3/2}

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

\frac{4 \cdot 2 ^{\frac{1}{2}}}{5} x^{\frac{5}{2}} + C

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply the Power Rule

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

= 2 \cdot 2^{\frac{1}{2}} \cdot \frac{2}{5} x^{\frac{5}{2}}

Simplify

2 \cdot 2^{\frac{1}{2}} \cdot \frac{2}{5} x^{\frac{5}{2}} : \frac{4 \cdot 2 ^{\frac{1}{2}}}{5} x^{\frac{5}{2}}

= \frac{4 \cdot 2 ^{\frac{1}{2}}}{5} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{4 \cdot 2 ^{\frac{1}{2}}}{5} x^{\frac{5}{2}} + C

\int t^{3} + t d t

\int y (1 - y) d y

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

\int \frac{y}{ln ( y )} d y

\int e^{x} 3 x d x

What is the integral of (2x)^{3/2} ?
The integral of (2x)^{3/2} is (4*2^{1/2})/5 x^{5/2}+C