3.1 \(\int 0 \, dx\)

Optimal. Leaf size=1 \[ 0 \]

[Out]

0

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Rubi [A]  time = 0.0000911, antiderivative size = 1, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 1, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 1., Rules used = {8} \[ 0 \]

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*}

Mathematica [A]  time = 0.0000228, size = 1, normalized size = 1. \[ 0 \]

Antiderivative was successfully verified.

[In]

Integrate[0,x]

[Out]

0

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Maple [A]  time = 0., size = 2, normalized size = 2. \begin{align*} 0 \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(0,x)

[Out]

0

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Maxima [A]  time = 1.01215, size = 1, normalized size = 1. \begin{align*} 0 \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(0,x, algorithm="maxima")

[Out]

0

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Fricas [A]  time = 1.61545, size = 4, normalized size = 4. \begin{align*} 0 \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(0,x, algorithm="fricas")

[Out]

0

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Sympy [A]  time = 0.011118, size = 0, normalized size = 0. \begin{align*} 0 \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(0,x)

[Out]

0

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Giac [A]  time = 1.0815, size = 1, normalized size = 1. \begin{align*} 0 \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(0,x, algorithm="giac")

[Out]

0