3.99.17 \(\int -\frac {\log (6)}{2} \, dx\)

Optimal. Leaf size=7 \[ -\frac {1}{2} x \log (6) \]

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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 = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {8} \begin {gather*} -\frac {1}{2} x \log (6) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-1/2*Log[6],x]

[Out]

-1/2*(x*Log[6])

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\frac {1}{2} x \log (6)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 7, normalized size = 1.00 \begin {gather*} -\frac {1}{2} x \log (6) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-1/2*Log[6],x]

[Out]

-1/2*(x*Log[6])

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fricas [A]  time = 0.75, size = 5, normalized size = 0.71 \begin {gather*} -\frac {1}{2} \, x \log \relax (6) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/2*log(6),x, algorithm="fricas")

[Out]

-1/2*x*log(6)

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giac [A]  time = 0.18, size = 5, normalized size = 0.71 \begin {gather*} -\frac {1}{2} \, x \log \relax (6) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/2*log(6),x, algorithm="giac")

[Out]

-1/2*x*log(6)

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maple [A]  time = 0.02, size = 6, normalized size = 0.86

method	result	size
default	\(-\frac {x \ln \relax (6)}{2}\)	\(6\)
norman	\(-\frac {x \ln \relax (6)}{2}\)	\(6\)
risch	\(-\frac {x \ln \relax (2)}{2}-\frac {x \ln \relax (3)}{2}\)	\(12\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-1/2*ln(6),x,method=_RETURNVERBOSE)

[Out]

-1/2*x*ln(6)

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maxima [A]  time = 0.34, size = 5, normalized size = 0.71 \begin {gather*} -\frac {1}{2} \, x \log \relax (6) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/2*log(6),x, algorithm="maxima")

[Out]

-1/2*x*log(6)

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mupad [B]  time = 0.00, size = 5, normalized size = 0.71 \begin {gather*} -\frac {x\,\ln \relax (6)}{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-log(6)/2,x)

[Out]

-(x*log(6))/2

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sympy [A]  time = 0.01, size = 7, normalized size = 1.00 \begin {gather*} - \frac {x \log {\relax (6 )}}{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/2*ln(6),x)

[Out]

-x*log(6)/2

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