Optimal. Leaf size=28 \[ 4 \log \left (2 e^{-\frac {x}{\log (8)}}-4 x+\frac {4}{3 (4+\log (x))}\right ) \]
________________________________________________________________________________________
Rubi [F] time = 7.90, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {192 x+e^{\frac {x}{\log (8)}} (8+384 x) \log (8)+\left (96 x+192 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log (x)+\left (12 x+24 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log ^2(x)}{-48 x \log (8)+e^{\frac {x}{\log (8)}} \left (-8 x+96 x^2\right ) \log (8)+\left (-24 x \log (8)+e^{\frac {x}{\log (8)}} \left (-2 x+48 x^2\right ) \log (8)\right ) \log (x)+\left (-3 x \log (8)+6 e^{\frac {x}{\log (8)}} x^2 \log (8)\right ) \log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-192 x-e^{\frac {x}{\log (8)}} (8+384 x) \log (8)-\left (96 x+192 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log (x)-\left (12 x+24 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log ^2(x)}{x \log (8) (4+\log (x)) \left (12+2 e^{\frac {x}{\log (8)}}-24 e^{\frac {x}{\log (8)}} x+3 \log (x)-6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx\\ &=\frac {\int \frac {-192 x-e^{\frac {x}{\log (8)}} (8+384 x) \log (8)-\left (96 x+192 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log (x)-\left (12 x+24 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log ^2(x)}{x (4+\log (x)) \left (12+2 e^{\frac {x}{\log (8)}}-24 e^{\frac {x}{\log (8)}} x+3 \log (x)-6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}\\ &=\frac {\int \left (\frac {4 \log (8) \left (1+48 x+24 x \log (x)+3 x \log ^2(x)\right )}{x (4+\log (x)) (-1+12 x+3 x \log (x))}+\frac {12 \left (48 x^2-4 x (1-12 \log (8))+\log (8)+24 x^2 \log (x)-x (1-24 \log (8)) \log (x)+3 x^2 \log ^2(x)+3 x \log (8) \log ^2(x)\right )}{x (1-12 x-3 x \log (x)) \left (12+2 e^{\frac {x}{\log (8)}}-24 e^{\frac {x}{\log (8)}} x+3 \log (x)-6 e^{\frac {x}{\log (8)}} x \log (x)\right )}\right ) \, dx}{\log (8)}\\ &=4 \int \frac {1+48 x+24 x \log (x)+3 x \log ^2(x)}{x (4+\log (x)) (-1+12 x+3 x \log (x))} \, dx+\frac {12 \int \frac {48 x^2-4 x (1-12 \log (8))+\log (8)+24 x^2 \log (x)-x (1-24 \log (8)) \log (x)+3 x^2 \log ^2(x)+3 x \log (8) \log ^2(x)}{x (1-12 x-3 x \log (x)) \left (12+2 e^{\frac {x}{\log (8)}}-24 e^{\frac {x}{\log (8)}} x+3 \log (x)-6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}\\ &=4 \int \left (\frac {1}{x}-\frac {1}{x (4+\log (x))}+\frac {1+3 x}{x (-1+12 x+3 x \log (x))}\right ) \, dx+\frac {12 \int \left (\frac {48 x}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )}+\frac {\log (8)}{x (-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )}+\frac {4 (-1+12 \log (8))}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )}+\frac {24 x \log (x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )}+\frac {(-1+24 \log (8)) \log (x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )}+\frac {3 x \log ^2(x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )}+\frac {3 \log (8) \log ^2(x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )}\right ) \, dx}{\log (8)}\\ &=4 \log (x)-4 \int \frac {1}{x (4+\log (x))} \, dx+4 \int \frac {1+3 x}{x (-1+12 x+3 x \log (x))} \, dx+12 \int \frac {1}{x (-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx+36 \int \frac {\log ^2(x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx+\frac {36 \int \frac {x \log ^2(x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}+\frac {288 \int \frac {x \log (x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}+\frac {576 \int \frac {x}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}-\frac {(48 (1-12 \log (8))) \int \frac {1}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}+\frac {(12 (-1+24 \log (8))) \int \frac {\log (x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}\\ &=4 \log (x)+4 \int \left (\frac {3}{-1+12 x+3 x \log (x)}+\frac {1}{x (-1+12 x+3 x \log (x))}\right ) \, dx-4 \operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,4+\log (x)\right )+12 \int \frac {1}{x (-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx+36 \int \frac {\log ^2(x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx+\frac {36 \int \frac {x \log ^2(x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}+\frac {288 \int \frac {x \log (x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}+\frac {576 \int \frac {x}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}-\frac {(48 (1-12 \log (8))) \int \frac {1}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}+\frac {(12 (-1+24 \log (8))) \int \frac {\log (x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}\\ &=4 \log (x)-4 \log (4+\log (x))+4 \int \frac {1}{x (-1+12 x+3 x \log (x))} \, dx+12 \int \frac {1}{-1+12 x+3 x \log (x)} \, dx+12 \int \frac {1}{x (-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx+36 \int \frac {\log ^2(x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx+\frac {36 \int \frac {x \log ^2(x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}+\frac {288 \int \frac {x \log (x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}+\frac {576 \int \frac {x}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}-\frac {(48 (1-12 \log (8))) \int \frac {1}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}+\frac {(12 (-1+24 \log (8))) \int \frac {\log (x)}{(-1+12 x+3 x \log (x)) \left (-12-2 e^{\frac {x}{\log (8)}}+24 e^{\frac {x}{\log (8)}} x-3 \log (x)+6 e^{\frac {x}{\log (8)}} x \log (x)\right )} \, dx}{\log (8)}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [F] time = 0.78, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {192 x+e^{\frac {x}{\log (8)}} (8+384 x) \log (8)+\left (96 x+192 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log (x)+\left (12 x+24 e^{\frac {x}{\log (8)}} x \log (8)\right ) \log ^2(x)}{-48 x \log (8)+e^{\frac {x}{\log (8)}} \left (-8 x+96 x^2\right ) \log (8)+\left (-24 x \log (8)+e^{\frac {x}{\log (8)}} \left (-2 x+48 x^2\right ) \log (8)\right ) \log (x)+\left (-3 x \log (8)+6 e^{\frac {x}{\log (8)}} x^2 \log (8)\right ) \log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.70, size = 102, normalized size = 3.64 \begin {gather*} \frac {4 \, {\left (3 \, \log \relax (2) \log \relax (x) + 3 \, \log \relax (2) \log \left (\frac {2 \, {\left (12 \, x - 1\right )} e^{\left (\frac {x}{3 \, \log \relax (2)}\right )} + 3 \, {\left (2 \, x e^{\left (\frac {x}{3 \, \log \relax (2)}\right )} - 1\right )} \log \relax (x) - 12}{2 \, x e^{\left (\frac {x}{3 \, \log \relax (2)}\right )} - 1}\right ) + 3 \, \log \relax (2) \log \left (\frac {2 \, x e^{\left (\frac {x}{3 \, \log \relax (2)}\right )} - 1}{x}\right ) - 3 \, \log \relax (2) \log \left (\log \relax (x) + 4\right ) - x\right )}}{3 \, \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 2.63, size = 94, normalized size = 3.36 \begin {gather*} \frac {4 \, {\left (3 \, \log \relax (2) \log \left (6 \, x e^{\left (\frac {x}{3 \, \log \relax (2)}\right )} \log \relax (x) + 24 \, x e^{\left (\frac {x}{3 \, \log \relax (2)}\right )} - 2 \, e^{\left (\frac {x}{3 \, \log \relax (2)}\right )} - 3 \, \log \relax (x) - 12\right ) + 3 \, \log \relax (2) \log \left (3 \, x \log \relax (x) + 12 \, x - 1\right ) - 3 \, \log \relax (2) \log \left (-3 \, x \log \relax (x) - 12 \, x + 1\right ) - 3 \, \log \relax (2) \log \left (\log \relax (x) + 4\right ) - x\right )}}{3 \, \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.40, size = 59, normalized size = 2.11
method | result | size |
norman | \(-\frac {4 x}{3 \ln \relax (2)}-4 \ln \left (\ln \relax (x )+4\right )+4 \ln \left (6 \ln \relax (x ) {\mathrm e}^{\frac {x}{3 \ln \relax (2)}} x +24 x \,{\mathrm e}^{\frac {x}{3 \ln \relax (2)}}-2 \,{\mathrm e}^{\frac {x}{3 \ln \relax (2)}}-3 \ln \relax (x )-12\right )\) | \(59\) |
risch | \(4 \ln \relax (x )+4 \ln \left ({\mathrm e}^{\frac {x}{3 \ln \relax (2)}}-\frac {1}{2 x}\right )-\frac {4 x}{3 \ln \relax (2)}+4 \ln \left (\ln \relax (x )+\frac {8 x \,{\mathrm e}^{\frac {x}{3 \ln \relax (2)}}-\frac {2 \,{\mathrm e}^{\frac {x}{3 \ln \relax (2)}}}{3}-4}{2 x \,{\mathrm e}^{\frac {x}{3 \ln \relax (2)}}-1}\right )-4 \ln \left (\ln \relax (x )+4\right )\) | \(83\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.76, size = 80, normalized size = 2.86 \begin {gather*} -\frac {4 \, x}{3 \, \log \relax (2)} + 4 \, \log \relax (x) + 4 \, \log \left (\frac {2 \, {\left (3 \, x \log \relax (x) + 12 \, x - 1\right )} e^{\left (\frac {x}{3 \, \log \relax (2)}\right )} - 3 \, \log \relax (x) - 12}{2 \, {\left (3 \, x \log \relax (x) + 12 \, x - 1\right )}}\right ) + 4 \, \log \left (\frac {3 \, x \log \relax (x) + 12 \, x - 1}{3 \, x}\right ) - 4 \, \log \left (\log \relax (x) + 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {\left (12\,x+72\,x\,{\mathrm {e}}^{\frac {x}{3\,\ln \relax (2)}}\,\ln \relax (2)\right )\,{\ln \relax (x)}^2+\left (96\,x+576\,x\,{\mathrm {e}}^{\frac {x}{3\,\ln \relax (2)}}\,\ln \relax (2)\right )\,\ln \relax (x)+192\,x+3\,{\mathrm {e}}^{\frac {x}{3\,\ln \relax (2)}}\,\ln \relax (2)\,\left (384\,x+8\right )}{\left (9\,x\,\ln \relax (2)-18\,x^2\,{\mathrm {e}}^{\frac {x}{3\,\ln \relax (2)}}\,\ln \relax (2)\right )\,{\ln \relax (x)}^2+\left (72\,x\,\ln \relax (2)+3\,{\mathrm {e}}^{\frac {x}{3\,\ln \relax (2)}}\,\ln \relax (2)\,\left (2\,x-48\,x^2\right )\right )\,\ln \relax (x)+144\,x\,\ln \relax (2)+3\,{\mathrm {e}}^{\frac {x}{3\,\ln \relax (2)}}\,\ln \relax (2)\,\left (8\,x-96\,x^2\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 4.10, size = 71, normalized size = 2.54 \begin {gather*} \frac {- 4 x + 12 \log {\relax (2 )} \log {\relax (x )}}{3 \log {\relax (2 )}} + 4 \log {\left (\frac {- 3 \log {\relax (x )} - 12}{6 x \log {\relax (x )} + 24 x - 2} + e^{\frac {x}{3 \log {\relax (2 )}}} \right )} - 4 \log {\left (\log {\relax (x )} + 4 \right )} + 4 \log {\left (\log {\relax (x )} + \frac {96 x - 8}{24 x} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________