3.27.42 \(\int -\frac {\log (3)}{3} \, dx\)

Optimal. Leaf size=7 \[ -\frac {1}{3} x \log (3) \]

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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 = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {8} \begin {gather*} -\frac {1}{3} x \log (3) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-1/3*Log[3],x]

[Out]

-1/3*(x*Log[3])

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\frac {1}{3} x \log (3)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 7, normalized size = 1.00 \begin {gather*} -\frac {1}{3} x \log (3) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-1/3*Log[3],x]

[Out]

-1/3*(x*Log[3])

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fricas [A]  time = 0.55, size = 5, normalized size = 0.71 \begin {gather*} -\frac {1}{3} \, x \log \relax (3) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/3*log(3),x, algorithm="fricas")

[Out]

-1/3*x*log(3)

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giac [A]  time = 0.19, size = 5, normalized size = 0.71 \begin {gather*} -\frac {1}{3} \, x \log \relax (3) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/3*log(3),x, algorithm="giac")

[Out]

-1/3*x*log(3)

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maple [A]  time = 0.01, size = 6, normalized size = 0.86

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-1/3*ln(3),x,method=_RETURNVERBOSE)

[Out]

-1/3*x*ln(3)

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maxima [A]  time = 0.35, size = 5, normalized size = 0.71 \begin {gather*} -\frac {1}{3} \, x \log \relax (3) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/3*log(3),x, algorithm="maxima")

[Out]

-1/3*x*log(3)

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mupad [B]  time = 0.00, size = 5, normalized size = 0.71 \begin {gather*} -\frac {x\,\ln \relax (3)}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-log(3)/3,x)

[Out]

-(x*log(3))/3

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sympy [A]  time = 0.01, size = 7, normalized size = 1.00 \begin {gather*} - \frac {x \log {\relax (3 )}}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/3*ln(3),x)

[Out]

-x*log(3)/3

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