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Popular >

integral of (x^2)/3

Solution

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

Solution

\frac{x ^{3}}{9} + C

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Simplify

\frac{1}{3} \cdot \frac{x ^{3}}{3} : \frac{x ^{3}}{9}

= \frac{x ^{3}}{9}

Add a constant to the solution

= \frac{x ^{3}}{9} + C

Popular Examples

integral of x/(3x^4+1)

\int \frac{x}{3 x ^{4} + 1} d x

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

\int (x ln (2) + \frac{3}{2 x}) d x

derivative of f(x)=sqrt(x-6)derivative of

f (x) = x - 6

derivative of f(x)=3e^{2x^2}derivative of

f (x) = 3 e^{2 x^{2}}

integral from-2 to 0 of (5x^2+5x)

\int_{- 2}^{0} (5 x^{2} + 5 x) d x

Frequently Asked Questions (FAQ)

What is the integral of (x^2)/3 ?
The integral of (x^2)/3 is (x^3)/9+C