en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x)^3

Solution

integral

(2 x)^{3}

Solution

2 x^{4} + C

Solution steps

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

Simplify

(2 x)^{3} : 8 x^{3}

= \int 8 x^{3} d x

Take the constant out:

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

= 8 \cdot \int x^{3} d x

Apply the Power Rule

: \frac{x ^{4}}{4}

= 8 \cdot \frac{x ^{4}}{4}

Simplify

8 \cdot \frac{x ^{4}}{4} : 2 x^{4}

= 2 x^{4}

Add a constant to the solution

= 2 x^{4} + C

Graph

Popular Examples

integral of 1/((x^2+2x)^{1/2)}integral

\frac{1}{( x ^{2} + 2 x ) ^{\frac{1}{2}}}

integral of ((x+2))/((x^2+3x))integral

\frac{( x + 2 )}{( x ^{2} + 3 x )}

integral of v/2 integral

\frac{v}{2}

integral of ((x-1))/((x^2+2x+3))integral

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

integral of 1/(x(x^2-1))integral

\frac{1}{x ( x ^{2} - 1 )}

Frequently Asked Questions (FAQ)

What is the integral of (2x)^3 ?
The integral of (2x)^3 is 2x^4+C