\(\int -\log (5) \, dx\) [740]

Optimal result

Integrand size = 4, antiderivative size = 17 \[ \int -\log (5) \, dx=5-x \log (5)-\frac {4}{5 \log (5 e)} \]

[Out]

5-4/5/ln(5*exp(1))-x*ln(5)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.29, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {8} \[ \int -\log (5) \, dx=-x \log (5) \]

[In]

Int[-Log[5],x]

[Out]

-(x*Log[5])

Rule 8

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

Rubi steps \begin{align*} \text {integral}& = -x \log (5) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.29 \[ \int -\log (5) \, dx=-x \log (5) \]

[In]

Integrate[-Log[5],x]

[Out]

-(x*Log[5])

Maple [A] (verified)

Time = 0.01 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.35

method	result	size
default	\(-x \ln \left (5\right )\)	\(6\)
norman	\(-x \ln \left (5\right )\)	\(6\)
risch	\(-x \ln \left (5\right )\)	\(6\)
parallelrisch	\(-x \ln \left (5\right )\)	\(6\)

[In]

int(-ln(5),x,method=_RETURNVERBOSE)

[Out]

-x*ln(5)

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.29 \[ \int -\log (5) \, dx=-x \log \left (5\right ) \]

[In]

integrate(-log(5),x, algorithm="fricas")

[Out]

-x*log(5)

Sympy [A] (verification not implemented)

Time = 0.01 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.29 \[ \int -\log (5) \, dx=- x \log {\left (5 \right )} \]

[In]

integrate(-ln(5),x)

[Out]

-x*log(5)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.29 \[ \int -\log (5) \, dx=-x \log \left (5\right ) \]

[In]

integrate(-log(5),x, algorithm="maxima")

[Out]

-x*log(5)

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.29 \[ \int -\log (5) \, dx=-x \log \left (5\right ) \]

[In]

integrate(-log(5),x, algorithm="giac")

[Out]

-x*log(5)

Mupad [B] (verification not implemented)

Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.29 \[ \int -\log (5) \, dx=-x\,\ln \left (5\right ) \]

[In]

int(-log(5),x)

[Out]

-x*log(5)