en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x(2x)

Solution

\int x (2 x) d x

Solution

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

Solution steps

\int x \cdot 2 x d x

Take the constant out:

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

= 2 \cdot \int xx d x

Simplify

xx : x^{2}

= 2 \cdot \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Add a constant to the solution

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

Popular Examples

integral of x_{1}

\int x_{1} d x

integral of 1/((1+\sqrt[3]{x+1))}

integral of (2t)/(t^2+4)

\int \frac{2 t}{t ^{2} + 4} d t

integral of 3x^2(2x^3+4)^7

\int 3 x^{2} (2 x^{3} + 4)^{7} d x

integral of (5x^3-7x+4)/(x^3-x^2)

\int \frac{5 x ^{3} - 7 x + 4}{x ^{3} - x ^{2}} d x

Frequently Asked Questions (FAQ)

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