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

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

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integral of ((x^3)/3)

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

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

Solution steps

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

x^{3} - 2 x^{2} + 2, 3 x^{2} + 5 x - 23

\frac{d}{d x} (\frac{1}{cot ( x )} - cot (x))

x \to - 3 lim (\frac{1}{2 x + 3})

x \to 3 lim (1 + \frac{1}{x})

x \to 3 - lim (\frac{1}{( x ^{2} - 9 )})