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Popular >

integral of 1/3 x^3

Solution

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

Solution

\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

Popular Examples

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\frac{d}{d x} (\frac{3}{5 x ^{\frac{2}{5}}})

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

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

Frequently Asked Questions (FAQ)

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