3.51.46 \(\int \frac {20 \log (4 e^5)}{e^{10}} \, dx\)

Optimal. Leaf size=12 \[ \frac {20 x \log \left (4 e^5\right )}{e^{10}} \]

________________________________________________________________________________________

Rubi [A]  time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.83, number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {8} \begin {gather*} \frac {20 x (5+\log (4))}{e^{10}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(20*Log[4*E^5])/E^10,x]

[Out]

(20*x*(5 + Log[4]))/E^10

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {20 x (5+\log (4))}{e^{10}}\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 12, normalized size = 1.00 \begin {gather*} \frac {20 x \log \left (4 e^5\right )}{e^{10}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(20*Log[4*E^5])/E^10,x]

[Out]

(20*x*Log[4*E^5])/E^10

________________________________________________________________________________________

fricas [A]  time = 0.69, size = 13, normalized size = 1.08 \begin {gather*} 20 \, {\left (2 \, x \log \relax (2) + 5 \, x\right )} e^{\left (-10\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(20*log(4*exp(5))/exp(10),x, algorithm="fricas")

[Out]

20*(2*x*log(2) + 5*x)*e^(-10)

________________________________________________________________________________________

giac [A]  time = 0.15, size = 10, normalized size = 0.83 \begin {gather*} 20 \, x e^{\left (-10\right )} \log \left (4 \, e^{5}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(20*log(4*exp(5))/exp(10),x, algorithm="giac")

[Out]

20*x*e^(-10)*log(4*e^5)

________________________________________________________________________________________

maple [A]  time = 0.02, size = 13, normalized size = 1.08

method	result	size
default	\(20 \,{\mathrm e}^{-10} x \ln \left (4 \,{\mathrm e}^{5}\right )\)	\(13\)
norman	\(20 \left (2 \ln \relax (2)+5\right ) {\mathrm e}^{-10} x\)	\(14\)
risch	\(40 \,{\mathrm e}^{-10} x \ln \relax (2)+100 \,{\mathrm e}^{-10} x\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(20*ln(4*exp(5))/exp(10),x,method=_RETURNVERBOSE)

[Out]

20/exp(10)*x*ln(4*exp(5))

________________________________________________________________________________________

maxima [A]  time = 0.34, size = 10, normalized size = 0.83 \begin {gather*} 20 \, x e^{\left (-10\right )} \log \left (4 \, e^{5}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(20*log(4*exp(5))/exp(10),x, algorithm="maxima")

[Out]

20*x*e^(-10)*log(4*e^5)

________________________________________________________________________________________

mupad [B]  time = 0.00, size = 10, normalized size = 0.83 \begin {gather*} 20\,x\,\ln \left (4\,{\mathrm {e}}^5\right )\,{\mathrm {e}}^{-10} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(20*log(4*exp(5))*exp(-10),x)

[Out]

20*x*log(4*exp(5))*exp(-10)

________________________________________________________________________________________

sympy [A]  time = 0.05, size = 12, normalized size = 1.00 \begin {gather*} \frac {20 x \log {\left (4 e^{5} \right )}}{e^{10}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(20*ln(4*exp(5))/exp(10),x)

[Out]

20*x*exp(-10)*log(4*exp(5))

________________________________________________________________________________________