3.12 \(\int x^2 \, dx\)

Optimal. Leaf size=7 \[ \frac{x^3}{3} \]

[Out]

x^3/3

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Rubi [A]  time = 0.0004105, antiderivative size = 7, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 3, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333, Rules used = {30} \[ \frac{x^3}{3} \]

Antiderivative was successfully verified.

[In]

Int[x^2,x]

[Out]

x^3/3

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps

\begin{align*} \int x^2 \, dx &=\frac{x^3}{3}\\ \end{align*}

Mathematica [A]  time = 0.0000218, size = 7, normalized size = 1. \[ \frac{x^3}{3} \]

Antiderivative was successfully verified.

[In]

Integrate[x^2,x]

[Out]

x^3/3

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Maple [A]  time = 0.002, size = 6, normalized size = 0.9 \begin{align*}{\frac{{x}^{3}}{3}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^2,x)

[Out]

1/3*x^3

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Maxima [A]  time = 0.976844, size = 7, normalized size = 1. \begin{align*} \frac{1}{3} \, x^{3} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^2,x, algorithm="maxima")

[Out]

1/3*x^3

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Fricas [A]  time = 1.32392, size = 12, normalized size = 1.71 \begin{align*} \frac{1}{3} x^{3} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^2,x, algorithm="fricas")

[Out]

1/3*x^3

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Sympy [A]  time = 0.047793, size = 3, normalized size = 0.43 \begin{align*} \frac{x^{3}}{3} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**2,x)

[Out]

x**3/3

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Giac [A]  time = 1.27413, size = 7, normalized size = 1. \begin{align*} \frac{1}{3} \, x^{3} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^2,x, algorithm="giac")

[Out]

1/3*x^3