Optimal. Leaf size=28 \[ \log \left (-\frac {e^5}{x}+x+4 x \left (-e^{\frac {x}{\log (4)}}+x\right )^4\right ) \]
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Rubi [F] time = 19.48, 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 {\left (e^5+x^2+20 x^6\right ) \log (4)+e^{\frac {4 x}{\log (4)}} \left (16 x^3+4 x^2 \log (4)\right )+e^{\frac {3 x}{\log (4)}} \left (-48 x^4-32 x^3 \log (4)\right )+e^{\frac {2 x}{\log (4)}} \left (48 x^5+72 x^4 \log (4)\right )+e^{\frac {x}{\log (4)}} \left (-16 x^6-64 x^5 \log (4)\right )}{4 e^{\frac {4 x}{\log (4)}} x^3 \log (4)-16 e^{\frac {3 x}{\log (4)}} x^4 \log (4)+24 e^{\frac {2 x}{\log (4)}} x^5 \log (4)-16 e^{\frac {x}{\log (4)}} x^6 \log (4)+\left (-e^5 x+x^3+4 x^7\right ) \log (4)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-\left (\left (e^5+x^2+20 x^6\right ) \log (4)\right )-e^{\frac {4 x}{\log (4)}} \left (16 x^3+4 x^2 \log (4)\right )-e^{\frac {3 x}{\log (4)}} \left (-48 x^4-32 x^3 \log (4)\right )-e^{\frac {2 x}{\log (4)}} \left (48 x^5+72 x^4 \log (4)\right )-e^{\frac {x}{\log (4)}} \left (-16 x^6-64 x^5 \log (4)\right )}{x \left (e^5-x^2-4 e^{\frac {4 x}{\log (4)}} x^2+16 e^{\frac {3 x}{\log (4)}} x^3-24 e^{\frac {2 x}{\log (4)}} x^4+16 e^{\frac {x}{\log (4)}} x^5-4 x^6\right ) \log (4)} \, dx\\ &=\frac {\int \frac {-\left (\left (e^5+x^2+20 x^6\right ) \log (4)\right )-e^{\frac {4 x}{\log (4)}} \left (16 x^3+4 x^2 \log (4)\right )-e^{\frac {3 x}{\log (4)}} \left (-48 x^4-32 x^3 \log (4)\right )-e^{\frac {2 x}{\log (4)}} \left (48 x^5+72 x^4 \log (4)\right )-e^{\frac {x}{\log (4)}} \left (-16 x^6-64 x^5 \log (4)\right )}{x \left (e^5-x^2-4 e^{\frac {4 x}{\log (4)}} x^2+16 e^{\frac {3 x}{\log (4)}} x^3-24 e^{\frac {2 x}{\log (4)}} x^4+16 e^{\frac {x}{\log (4)}} x^5-4 x^6\right )} \, dx}{\log (4)}\\ &=\frac {\int \left (\frac {4 x+\log (4)}{x}-\frac {2 \left (-2 e^5 x+2 x^3-8 e^{\frac {3 x}{\log (4)}} x^4+24 e^{\frac {2 x}{\log (4)}} x^5-24 e^{\frac {x}{\log (4)}} x^6+8 x^7-e^5 \log (4)+8 e^{\frac {3 x}{\log (4)}} x^3 \log (4)-24 e^{\frac {2 x}{\log (4)}} x^4 \log (4)+24 e^{\frac {x}{\log (4)}} x^5 \log (4)-8 x^6 \log (4)\right )}{x \left (-e^5+x^2+4 e^{\frac {4 x}{\log (4)}} x^2-16 e^{\frac {3 x}{\log (4)}} x^3+24 e^{\frac {2 x}{\log (4)}} x^4-16 e^{\frac {x}{\log (4)}} x^5+4 x^6\right )}\right ) \, dx}{\log (4)}\\ &=\frac {\int \frac {4 x+\log (4)}{x} \, dx}{\log (4)}-\frac {2 \int \frac {-2 e^5 x+2 x^3-8 e^{\frac {3 x}{\log (4)}} x^4+24 e^{\frac {2 x}{\log (4)}} x^5-24 e^{\frac {x}{\log (4)}} x^6+8 x^7-e^5 \log (4)+8 e^{\frac {3 x}{\log (4)}} x^3 \log (4)-24 e^{\frac {2 x}{\log (4)}} x^4 \log (4)+24 e^{\frac {x}{\log (4)}} x^5 \log (4)-8 x^6 \log (4)}{x \left (-e^5+x^2+4 e^{\frac {4 x}{\log (4)}} x^2-16 e^{\frac {3 x}{\log (4)}} x^3+24 e^{\frac {2 x}{\log (4)}} x^4-16 e^{\frac {x}{\log (4)}} x^5+4 x^6\right )} \, dx}{\log (4)}\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [F] time = 1.81, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (e^5+x^2+20 x^6\right ) \log (4)+e^{\frac {4 x}{\log (4)}} \left (16 x^3+4 x^2 \log (4)\right )+e^{\frac {3 x}{\log (4)}} \left (-48 x^4-32 x^3 \log (4)\right )+e^{\frac {2 x}{\log (4)}} \left (48 x^5+72 x^4 \log (4)\right )+e^{\frac {x}{\log (4)}} \left (-16 x^6-64 x^5 \log (4)\right )}{4 e^{\frac {4 x}{\log (4)}} x^3 \log (4)-16 e^{\frac {3 x}{\log (4)}} x^4 \log (4)+24 e^{\frac {2 x}{\log (4)}} x^5 \log (4)-16 e^{\frac {x}{\log (4)}} x^6 \log (4)+\left (-e^5 x+x^3+4 x^7\right ) \log (4)} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.79, size = 72, normalized size = 2.57 \begin {gather*} \log \relax (x) + \log \left (\frac {4 \, x^{6} - 16 \, x^{5} e^{\left (\frac {x}{2 \, \log \relax (2)}\right )} + 24 \, x^{4} e^{\frac {x}{\log \relax (2)}} - 16 \, x^{3} e^{\left (\frac {3 \, x}{2 \, \log \relax (2)}\right )} + 4 \, x^{2} e^{\left (\frac {2 \, x}{\log \relax (2)}\right )} + x^{2} - e^{5}}{x^{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 5.56, size = 70, normalized size = 2.50 \begin {gather*} \log \left (4 \, x^{6} - 16 \, x^{5} e^{\left (\frac {x}{2 \, \log \relax (2)}\right )} + 24 \, x^{4} e^{\frac {x}{\log \relax (2)}} - 16 \, x^{3} e^{\left (\frac {3 \, x}{2 \, \log \relax (2)}\right )} + 4 \, x^{2} e^{\left (\frac {2 \, x}{\log \relax (2)}\right )} + x^{2} - e^{5}\right ) - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.17, size = 68, normalized size = 2.43
method | result | size |
risch | \(\ln \relax (x )+\ln \left ({\mathrm e}^{\frac {2 x}{\ln \relax (2)}}-4 x \,{\mathrm e}^{\frac {3 x}{2 \ln \relax (2)}}+6 x^{2} {\mathrm e}^{\frac {x}{\ln \relax (2)}}-4 x^{3} {\mathrm e}^{\frac {x}{2 \ln \relax (2)}}-\frac {-4 x^{6}-x^{2}+{\mathrm e}^{5}}{4 x^{2}}\right )\) | \(68\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.71, size = 75, normalized size = 2.68 \begin {gather*} 2 \, \log \relax (x) + \log \left (-\frac {4 \, x^{6} - 16 \, x^{5} e^{\left (\frac {x}{2 \, \log \relax (2)}\right )} + 24 \, x^{4} e^{\frac {x}{\log \relax (2)}} - 16 \, x^{3} e^{\left (\frac {3 \, x}{2 \, \log \relax (2)}\right )} + 4 \, x^{2} e^{\left (\frac {2 \, x}{\log \relax (2)}\right )} + x^{2} - e^{5}}{16 \, x^{3}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {2\,\ln \relax (2)\,\left (20\,x^6+x^2+{\mathrm {e}}^5\right )+{\mathrm {e}}^{\frac {2\,x}{\ln \relax (2)}}\,\left (16\,x^3+8\,\ln \relax (2)\,x^2\right )-{\mathrm {e}}^{\frac {3\,x}{2\,\ln \relax (2)}}\,\left (48\,x^4+64\,\ln \relax (2)\,x^3\right )-{\mathrm {e}}^{\frac {x}{2\,\ln \relax (2)}}\,\left (16\,x^6+128\,\ln \relax (2)\,x^5\right )+{\mathrm {e}}^{\frac {x}{\ln \relax (2)}}\,\left (48\,x^5+144\,\ln \relax (2)\,x^4\right )}{2\,\ln \relax (2)\,\left (4\,x^7+x^3-{\mathrm {e}}^5\,x\right )+8\,x^3\,{\mathrm {e}}^{\frac {2\,x}{\ln \relax (2)}}\,\ln \relax (2)+48\,x^5\,{\mathrm {e}}^{\frac {x}{\ln \relax (2)}}\,\ln \relax (2)-32\,x^4\,{\mathrm {e}}^{\frac {3\,x}{2\,\ln \relax (2)}}\,\ln \relax (2)-32\,x^6\,{\mathrm {e}}^{\frac {x}{2\,\ln \relax (2)}}\,\ln \relax (2)} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.21, size = 68, normalized size = 2.43 \begin {gather*} \log {\relax (x )} + \log {\left (- 4 x^{3} e^{\frac {x}{2 \log {\relax (2 )}}} + 6 x^{2} e^{\frac {x}{\log {\relax (2 )}}} - 4 x e^{\frac {3 x}{2 \log {\relax (2 )}}} + e^{\frac {2 x}{\log {\relax (2 )}}} + \frac {4 x^{6} + x^{2} - e^{5}}{4 x^{2}} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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