\(\int -\frac {\log (3)}{3} \, dx\) [2642]

Optimal result

Integrand size = 6, antiderivative size = 7 \[ \int -\frac {\log (3)}{3} \, dx=-\frac {1}{3} x \log (3) \]

[Out]

-1/3*x*ln(3)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {8} \[ \int -\frac {\log (3)}{3} \, dx=-\frac {1}{3} x \log (3) \]

[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{align*} \text {integral}& = -\frac {1}{3} x \log (3) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.00 \[ \int -\frac {\log (3)}{3} \, dx=-\frac {1}{3} x \log (3) \]

[In]

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

[Out]

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

Maple [A] (verified)

Time = 0.00 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.86

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

[In]

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

[Out]

-1/3*x*ln(3)

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int -\frac {\log (3)}{3} \, dx=-\frac {1}{3} \, x \log \left (3\right ) \]

[In]

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

[Out]

-1/3*x*log(3)

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.00 \[ \int -\frac {\log (3)}{3} \, dx=- \frac {x \log {\left (3 \right )}}{3} \]

[In]

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

[Out]

-x*log(3)/3

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int -\frac {\log (3)}{3} \, dx=-\frac {1}{3} \, x \log \left (3\right ) \]

[In]

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

[Out]

-1/3*x*log(3)

Giac [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int -\frac {\log (3)}{3} \, dx=-\frac {1}{3} \, x \log \left (3\right ) \]

[In]

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

[Out]

-1/3*x*log(3)

Mupad [B] (verification not implemented)

Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int -\frac {\log (3)}{3} \, dx=-\frac {x\,\ln \left (3\right )}{3} \]

[In]

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

[Out]

-(x*log(3))/3