What is the integral of (1/3)x^3 ?

The integral of (1/3)x^3 is (x^4)/(12)+C

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integral of (1/3)x^3

\int (\frac{1}{3}) x^{3} d x

\frac{x ^{4}}{12} + C

Solution steps

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

Apply the Power Rule

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

= \frac{1}{3} \cdot \frac{x ^{4}}{4}

Simplify

\frac{1}{3} \cdot \frac{x ^{4}}{4} : \frac{x ^{4}}{12}

= \frac{x ^{4}}{12}

Add a constant to the solution

= \frac{x ^{4}}{12} + C

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