en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5/2 x^2

Solution

\int \frac{5}{2} x^{2} d x

Solution

\frac{5 x ^{3}}{6} + C

Solution steps

\int \frac{5}{2} x^{2} d x

Take the constant out:

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

= \frac{5}{2} \cdot \int x^{2} d x

Apply the Power Rule

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

= \frac{5}{2} \cdot \frac{x ^{3}}{3}

Simplify

\frac{5}{2} \cdot \frac{x ^{3}}{3} : \frac{5 x ^{3}}{6}

= \frac{5 x ^{3}}{6}

Add a constant to the solution

= \frac{5 x ^{3}}{6} + C

Popular Examples

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

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

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

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

integral of e^{4x}4

\int e^{4 x} 4 d x

integral of (3x^4-5sqrt(x)+1)

\int (3 x^{4} - 5 x + 1) d x

integral of (x^2+4\sqrt[3]{x})/x

Frequently Asked Questions (FAQ)

What is the integral of 5/2 x^2 ?
The integral of 5/2 x^2 is (5x^3)/6+C