3.1.1 \(\int 0 \, dx\)

Optimal. Leaf size=1 \[ 0 \]

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Rubi [A]  time = 0.00, antiderivative size = 1, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 1.000, Rules used = {8} \begin {gather*} 0 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[0,x]

[Out]

0

Rule 8

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]

Rubi steps

\begin {align*} \int 0 \, dx &=0\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 1, normalized size = 1.00 \begin {gather*} 0 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[0,x]

[Out]

0

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

Verification is not applicable to the result.

[In]

IntegrateAlgebraic[0,x]

[Out]

IntegrateAlgebraic[0, x]

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fricas [A]  time = 1.41, size = 1, normalized size = 1.00 \begin {gather*} 0 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(0,x, algorithm="fricas")

[Out]

0

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giac [A]  time = 1.09, size = 1, normalized size = 1.00 \begin {gather*} 0 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(0,x, algorithm="giac")

[Out]

0

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maple [A]  time = 0.00, size = 2, normalized size = 2.00 \begin {gather*} 0 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(0,x)

[Out]

0

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maxima [A]  time = 0.42, size = 1, normalized size = 1.00 \begin {gather*} 0 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(0,x, algorithm="maxima")

[Out]

0

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mupad [B]  time = 0.04, size = 1, normalized size = 1.00 \begin {gather*} 0 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(0,x)

[Out]

0

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sympy [A]  time = 0.01, size = 0, normalized size = 0.00 \begin {gather*} 0 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(0,x)

[Out]

0

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