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

Optimal. Leaf size=17 \[ 5-x \log (5)-\frac {4}{5 \log (5 e)} \]

[Out]

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

________________________________________________________________________________________

Rubi [A]
time = 0.00, antiderivative size = 5, normalized size of antiderivative = 0.29, number of steps used = 1, number of rules used = 1, integrand size = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {8} \begin {gather*} -x \log (5) \end {gather*}

Antiderivative was successfully verified.

[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 {gather*} \begin {aligned} \text {integral} &=-x \log (5)\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]
time = 0.00, size = 5, normalized size = 0.29 \begin {gather*} -x \log (5) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-Log[5],x]

[Out]

-(x*Log[5])

________________________________________________________________________________________

Maple [A]
time = 0.02, size = 6, normalized size = 0.35

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x*ln(5)

________________________________________________________________________________________

Maxima [A]
time = 0.28, size = 5, normalized size = 0.29 \begin {gather*} -x \log \left (5\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x*log(5)

________________________________________________________________________________________

Fricas [A]
time = 0.37, size = 5, normalized size = 0.29 \begin {gather*} -x \log \left (5\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x*log(5)

________________________________________________________________________________________

Sympy [A]
time = 0.00, size = 5, normalized size = 0.29 \begin {gather*} - x \log {\left (5 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-ln(5),x)

[Out]

-x*log(5)

________________________________________________________________________________________

Giac [A]
time = 0.41, size = 5, normalized size = 0.29 \begin {gather*} -x \log \left (5\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x*log(5)

________________________________________________________________________________________

Mupad [B]
time = 0.00, size = 5, normalized size = 0.29 \begin {gather*} -x\,\ln \left (5\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-log(5),x)

[Out]

-x*log(5)

________________________________________________________________________________________