3.1.5 \(\int -\frac {3}{2} \, dx\) [5]

Optimal. Leaf size=5 \[ -\frac {3 x}{2} \]

[Out]

-3/2*x

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Rubi [A]
time = 0.00, antiderivative size = 5, 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 = {8} \begin {gather*} -\frac {3 x}{2} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-3/2,x]

[Out]

(-3*x)/2

Rule 8

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

Rubi steps

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

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Mathematica [A]
time = 0.00, size = 5, normalized size = 1.00 \begin {gather*} -\frac {3 x}{2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-3/2,x]

[Out]

(-3*x)/2

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Maple [A]
time = 0.01, size = 4, normalized size = 0.80

method	result	size
default	\(-\frac {3 x}{2}\)	\(4\)
norman	\(-\frac {3 x}{2}\)	\(4\)
risch	\(-\frac {3 x}{2}\)	\(4\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-3/2,x,method=_RETURNVERBOSE)

[Out]

-3/2*x

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Maxima [A]
time = 0.28, size = 3, normalized size = 0.60 \begin {gather*} -\frac {3}{2} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/2,x, algorithm="maxima")

[Out]

-3/2*x

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Fricas [A]
time = 1.11, size = 3, normalized size = 0.60 \begin {gather*} -\frac {3}{2} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/2,x, algorithm="fricas")

[Out]

-3/2*x

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Sympy [A]
time = 0.00, size = 5, normalized size = 1.00 \begin {gather*} - \frac {3 x}{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/2,x)

[Out]

-3*x/2

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Giac [A]
time = 2.17, size = 3, normalized size = 0.60 \begin {gather*} -\frac {3}{2} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/2,x, algorithm="giac")

[Out]

-3/2*x

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Mupad [B]
time = 0.01, size = 3, normalized size = 0.60 \begin {gather*} -\frac {3\,x}{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-3/2,x)

[Out]

-(3*x)/2

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