en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x^2)/6

Solution

\int \frac{x ^{2}}{6} d x

Solution

\frac{x ^{3}}{18} + C

Solution steps

\int \frac{x ^{2}}{6} d x

Take the constant out:

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

= \frac{1}{6} \cdot \int x^{2} d x

Apply the Power Rule

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

= \frac{1}{6} \cdot \frac{x ^{3}}{3}

Simplify

\frac{1}{6} \cdot \frac{x ^{3}}{3} : \frac{x ^{3}}{18}

= \frac{x ^{3}}{18}

Add a constant to the solution

= \frac{x ^{3}}{18} + C

Popular Examples

derivative of cxcos(2x)

\frac{d}{d x} (c x cos (2 x))

integral of sqrt((4+9x)/4)

\int \frac{4 + 9 x}{4} d x

sum from n=1 to infinity of (0.9)^n

n = 1 \sum \infty (0.9)^{n}

25y^{''}-15y^'-4y=0

25 y^{^{''}} - 15 y^{^{'}} - 4 y = 0

derivative of f(x)=x^3(x^4-1)derivative of

f (x) = x^{3} (x^{4} - 1)

Frequently Asked Questions (FAQ)

What is the integral of (x^2)/6 ?
The integral of (x^2)/6 is (x^3)/(18)+C