3.102.91 \(\int \log (\frac {1}{6} (30-5 \log (\log (2))-15 e^3 (i \pi +\log (4-\log (3))))) \, dx\)

Optimal. Leaf size=34 \[ x \log \left (\frac {5}{2} \left (2-\frac {1}{3} \log (\log (2))-e^3 (i \pi +\log (4-\log (3)))\right )\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 32, normalized size of antiderivative = 0.94, number of steps used = 1, number of rules used = 1, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.033, Rules used = {8} \begin {gather*} x \log \left (\frac {5}{6} \left (6-\log (\log (2))-3 e^3 (\log (4-\log (3))+i \pi )\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[Log[(30 - 5*Log[Log[2]] - 15*E^3*(I*Pi + Log[4 - Log[3]]))/6],x]

[Out]

x*Log[(5*(6 - Log[Log[2]] - 3*E^3*(I*Pi + Log[4 - Log[3]])))/6]

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=x \log \left (\frac {5}{6} \left (6-\log (\log (2))-3 e^3 (i \pi +\log (4-\log (3)))\right )\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 32, normalized size = 0.94 \begin {gather*} x \log \left (\frac {1}{6} \left (30-5 \log (\log (2))-15 e^3 (i \pi +\log (4-\log (3)))\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[Log[(30 - 5*Log[Log[2]] - 15*E^3*(I*Pi + Log[4 - Log[3]]))/6],x]

[Out]

x*Log[(30 - 5*Log[Log[2]] - 15*E^3*(I*Pi + Log[4 - Log[3]]))/6]

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fricas [A]  time = 0.64, size = 19, normalized size = 0.56 \begin {gather*} x \log \left (-\frac {5}{2} \, e^{3} \log \left (\log \relax (3) - 4\right ) - \frac {5}{6} \, \log \left (\log \relax (2)\right ) + 5\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(-5/2*exp(3)*log(-4+log(3))-5/6*log(log(2))+5),x, algorithm="fricas")

[Out]

x*log(-5/2*e^3*log(log(3) - 4) - 5/6*log(log(2)) + 5)

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giac [A]  time = 0.16, size = 19, normalized size = 0.56 \begin {gather*} x \log \left (-\frac {5}{2} \, e^{3} \log \left (\log \relax (3) - 4\right ) - \frac {5}{6} \, \log \left (\log \relax (2)\right ) + 5\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(-5/2*exp(3)*log(-4+log(3))-5/6*log(log(2))+5),x, algorithm="giac")

[Out]

x*log(-5/2*e^3*log(log(3) - 4) - 5/6*log(log(2)) + 5)

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maple [A]  time = 0.10, size = 20, normalized size = 0.59

method	result	size
default	\(\ln \left (-\frac {5 \,{\mathrm e}^{3} \ln \left (-4+\ln \relax (3)\right )}{2}-\frac {5 \ln \left (\ln \relax (2)\right )}{6}+5\right ) x\)	\(20\)
norman	\(\left (\ln \left (\frac {5}{6}\right )+\ln \left (-3 \,{\mathrm e}^{3} \ln \left (-4+\ln \relax (3)\right )-\ln \left (\ln \relax (2)\right )+6\right )\right ) x\)	\(23\)
risch	\(x \ln \left (\frac {5}{6}\right )+x \ln \left (-3 \,{\mathrm e}^{3} \ln \left (-4+\ln \relax (3)\right )-\ln \left (\ln \relax (2)\right )+6\right )\)	\(25\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(ln(-5/2*exp(3)*ln(-4+ln(3))-5/6*ln(ln(2))+5),x,method=_RETURNVERBOSE)

[Out]

ln(-5/2*exp(3)*ln(-4+ln(3))-5/6*ln(ln(2))+5)*x

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maxima [A]  time = 0.35, size = 19, normalized size = 0.56 \begin {gather*} x \log \left (-\frac {5}{2} \, e^{3} \log \left (\log \relax (3) - 4\right ) - \frac {5}{6} \, \log \left (\log \relax (2)\right ) + 5\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(-5/2*exp(3)*log(-4+log(3))-5/6*log(log(2))+5),x, algorithm="maxima")

[Out]

x*log(-5/2*e^3*log(log(3) - 4) - 5/6*log(log(2)) + 5)

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mupad [B]  time = 0.00, size = 19, normalized size = 0.56 \begin {gather*} x\,\ln \left (5-\frac {5\,\ln \left (\ln \relax (3)-4\right )\,{\mathrm {e}}^3}{2}-\frac {5\,\ln \left (\ln \relax (2)\right )}{6}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(5 - (5*log(log(3) - 4)*exp(3))/2 - (5*log(log(2)))/6),x)

[Out]

x*log(5 - (5*log(log(3) - 4)*exp(3))/2 - (5*log(log(2)))/6)

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sympy [A]  time = 0.05, size = 29, normalized size = 0.85 \begin {gather*} x \log {\left (- \frac {5 \log {\left (\log {\relax (2 )} \right )}}{6} + 5 - \frac {5 \left (\log {\left (4 - \log {\relax (3 )} \right )} + i \pi \right ) e^{3}}{2} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(ln(-5/2*exp(3)*ln(-4+ln(3))-5/6*ln(ln(2))+5),x)

[Out]

x*log(-5*log(log(2))/6 + 5 - 5*(log(4 - log(3)) + I*pi)*exp(3)/2)

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