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

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

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Rubi [A]  time = 0.00, antiderivative size = 7, normalized size of antiderivative = 1.00, 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} \begin {gather*} \frac {x^3}{3} \end {gather*}

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*}

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Mathematica [A]  time = 0.00, size = 7, normalized size = 1.00 \begin {gather*} \frac {x^3}{3} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[x^2,x]

[Out]

x^3/3

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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x^2 \, dx \end {gather*}

Verification is not applicable to the result.

[In]

IntegrateAlgebraic[x^2,x]

[Out]

IntegrateAlgebraic[x^2, x]

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fricas [A]  time = 1.13, size = 5, normalized size = 0.71 \begin {gather*} \frac {1}{3} x^{3} \end {gather*}

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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giac [A]  time = 1.10, size = 5, normalized size = 0.71 \begin {gather*} \frac {1}{3} \, x^{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^2,x, algorithm="giac")

[Out]

1/3*x^3

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maple [A]  time = 0.00, size = 6, normalized size = 0.86 \begin {gather*} \frac {x^{3}}{3} \end {gather*}

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 = 0.42, size = 5, normalized size = 0.71 \begin {gather*} \frac {1}{3} \, x^{3} \end {gather*}

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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mupad [B]  time = 0.01, size = 5, normalized size = 0.71 \begin {gather*} \frac {x^3}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^2,x)

[Out]

x^3/3

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sympy [A]  time = 0.05, size = 3, normalized size = 0.43 \begin {gather*} \frac {x^{3}}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**2,x)

[Out]

x**3/3

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