Optimal. Leaf size=30 \[ 7+\left (-4 x+e^{5+\frac {3 \log (5)}{3-\log (x)}} x\right )^2-\log (x) \]
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Rubi [F] time = 6.90, 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 {-9+288 x^2+\left (6-192 x^2\right ) \log (x)+\left (-1+32 x^2\right ) \log ^2(x)+e^{\frac {-15-3 \log (5)+5 \log (x)}{-3+\log (x)}} \left (-144 x^2-24 x^2 \log (5)+96 x^2 \log (x)-16 x^2 \log ^2(x)\right )+e^{\frac {2 (-15-3 \log (5)+5 \log (x))}{-3+\log (x)}} \left (18 x^2+6 x^2 \log (5)-12 x^2 \log (x)+2 x^2 \log ^2(x)\right )}{9 x-6 x \log (x)+x \log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-9+288 x^2+\left (6-192 x^2\right ) \log (x)+\left (-1+32 x^2\right ) \log ^2(x)+e^{\frac {-15-3 \log (5)+5 \log (x)}{-3+\log (x)}} \left (-144 x^2-24 x^2 \log (5)+96 x^2 \log (x)-16 x^2 \log ^2(x)\right )+e^{\frac {2 (-15-3 \log (5)+5 \log (x))}{-3+\log (x)}} \left (18 x^2+6 x^2 \log (5)-12 x^2 \log (x)+2 x^2 \log ^2(x)\right )}{x (3-\log (x))^2} \, dx\\ &=\int \left (-\frac {9}{x (-3+\log (x))^2}+\frac {288 x}{(-3+\log (x))^2}-\frac {6 \left (-1+32 x^2\right ) \log (x)}{x (-3+\log (x))^2}+\frac {\left (-1+32 x^2\right ) \log ^2(x)}{x (-3+\log (x))^2}+\frac {8\ 5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}} \left (-18 \left (1+\frac {\log (5)}{6}\right )+12 \log (x)-2 \log ^2(x)\right )}{(3-\log (x))^2}+\frac {2\ 5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}} \left (9 \left (1+\frac {\log (5)}{3}\right )-6 \log (x)+\log ^2(x)\right )}{(3-\log (x))^2}\right ) \, dx\\ &=2 \int \frac {5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}} \left (9 \left (1+\frac {\log (5)}{3}\right )-6 \log (x)+\log ^2(x)\right )}{(3-\log (x))^2} \, dx-6 \int \frac {\left (-1+32 x^2\right ) \log (x)}{x (-3+\log (x))^2} \, dx+8 \int \frac {5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}} \left (-18 \left (1+\frac {\log (5)}{6}\right )+12 \log (x)-2 \log ^2(x)\right )}{(3-\log (x))^2} \, dx-9 \int \frac {1}{x (-3+\log (x))^2} \, dx+288 \int \frac {x}{(-3+\log (x))^2} \, dx+\int \frac {\left (-1+32 x^2\right ) \log ^2(x)}{x (-3+\log (x))^2} \, dx\\ &=\frac {288 x^2}{3-\log (x)}+2 \int \left (5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}}+\frac {3\ 5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}} \log (5)}{(-3+\log (x))^2}\right ) \, dx-6 \int \left (\frac {3 \left (-1+32 x^2\right )}{x (-3+\log (x))^2}+\frac {-1+32 x^2}{x (-3+\log (x))}\right ) \, dx+8 \int \left (-2 5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}}-\frac {3\ 5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}} \log (5)}{(-3+\log (x))^2}\right ) \, dx-9 \operatorname {Subst}\left (\int \frac {1}{x^2} \, dx,x,-3+\log (x)\right )+576 \int \frac {x}{-3+\log (x)} \, dx+\int \left (\frac {-1+32 x^2}{x}+\frac {9 \left (-1+32 x^2\right )}{x (-3+\log (x))^2}+\frac {6 \left (-1+32 x^2\right )}{x (-3+\log (x))}\right ) \, dx\\ &=-\frac {9}{3-\log (x)}+\frac {288 x^2}{3-\log (x)}+2 \int 5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}} \, dx+9 \int \frac {-1+32 x^2}{x (-3+\log (x))^2} \, dx-16 \int 5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}} \, dx-18 \int \frac {-1+32 x^2}{x (-3+\log (x))^2} \, dx+576 \operatorname {Subst}\left (\int \frac {e^{2 x}}{-3+x} \, dx,x,\log (x)\right )+(6 \log (5)) \int \frac {5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}}}{(-3+\log (x))^2} \, dx-(24 \log (5)) \int \frac {5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}}}{(-3+\log (x))^2} \, dx+\int \frac {-1+32 x^2}{x} \, dx\\ &=576 e^6 \text {Ei}(-2 (3-\log (x)))-\frac {9}{3-\log (x)}+\frac {288 x^2}{3-\log (x)}+2 \int 5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}} \, dx+9 \int \left (-\frac {1}{x (-3+\log (x))^2}+\frac {32 x}{(-3+\log (x))^2}\right ) \, dx-16 \int 5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}} \, dx-18 \int \left (-\frac {1}{x (-3+\log (x))^2}+\frac {32 x}{(-3+\log (x))^2}\right ) \, dx+(6 \log (5)) \int \frac {5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}}}{(-3+\log (x))^2} \, dx-(24 \log (5)) \int \frac {5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}}}{(-3+\log (x))^2} \, dx+\int \left (-\frac {1}{x}+32 x\right ) \, dx\\ &=16 x^2+576 e^6 \text {Ei}(-2 (3-\log (x)))-\frac {9}{3-\log (x)}+\frac {288 x^2}{3-\log (x)}-\log (x)+2 \int 5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}} \, dx-9 \int \frac {1}{x (-3+\log (x))^2} \, dx-16 \int 5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}} \, dx+18 \int \frac {1}{x (-3+\log (x))^2} \, dx+288 \int \frac {x}{(-3+\log (x))^2} \, dx-576 \int \frac {x}{(-3+\log (x))^2} \, dx+(6 \log (5)) \int \frac {5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}}}{(-3+\log (x))^2} \, dx-(24 \log (5)) \int \frac {5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}}}{(-3+\log (x))^2} \, dx\\ &=16 x^2+576 e^6 \text {Ei}(-2 (3-\log (x)))-\frac {9}{3-\log (x)}-\log (x)+2 \int 5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}} \, dx-9 \operatorname {Subst}\left (\int \frac {1}{x^2} \, dx,x,-3+\log (x)\right )-16 \int 5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}} \, dx+18 \operatorname {Subst}\left (\int \frac {1}{x^2} \, dx,x,-3+\log (x)\right )+576 \int \frac {x}{-3+\log (x)} \, dx-1152 \int \frac {x}{-3+\log (x)} \, dx+(6 \log (5)) \int \frac {5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}}}{(-3+\log (x))^2} \, dx-(24 \log (5)) \int \frac {5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}}}{(-3+\log (x))^2} \, dx\\ &=16 x^2+576 e^6 \text {Ei}(-2 (3-\log (x)))-\log (x)+2 \int 5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}} \, dx-16 \int 5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}} \, dx+576 \operatorname {Subst}\left (\int \frac {e^{2 x}}{-3+x} \, dx,x,\log (x)\right )-1152 \operatorname {Subst}\left (\int \frac {e^{2 x}}{-3+x} \, dx,x,\log (x)\right )+(6 \log (5)) \int \frac {5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}}}{(-3+\log (x))^2} \, dx-(24 \log (5)) \int \frac {5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}}}{(-3+\log (x))^2} \, dx\\ &=16 x^2-\log (x)+2 \int 5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}} \, dx-16 \int 5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}} \, dx+(6 \log (5)) \int \frac {5^{-\frac {6}{-3+\log (x)}} e^{-\frac {30}{-3+\log (x)}} x^{\frac {7+\log (x)}{-3+\log (x)}}}{(-3+\log (x))^2} \, dx-(24 \log (5)) \int \frac {5^{-\frac {3}{-3+\log (x)}} e^{-\frac {15}{-3+\log (x)}} x^{\frac {2+\log (x)}{-3+\log (x)}}}{(-3+\log (x))^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [F] time = 0.49, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {-9+288 x^2+\left (6-192 x^2\right ) \log (x)+\left (-1+32 x^2\right ) \log ^2(x)+e^{\frac {-15-3 \log (5)+5 \log (x)}{-3+\log (x)}} \left (-144 x^2-24 x^2 \log (5)+96 x^2 \log (x)-16 x^2 \log ^2(x)\right )+e^{\frac {2 (-15-3 \log (5)+5 \log (x))}{-3+\log (x)}} \left (18 x^2+6 x^2 \log (5)-12 x^2 \log (x)+2 x^2 \log ^2(x)\right )}{9 x-6 x \log (x)+x \log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.53, size = 57, normalized size = 1.90 \begin {gather*} -8 \, x^{2} e^{\left (-\frac {3 \, \log \relax (5) - 5 \, \log \relax (x) + 15}{\log \relax (x) - 3}\right )} + x^{2} e^{\left (-\frac {2 \, {\left (3 \, \log \relax (5) - 5 \, \log \relax (x) + 15\right )}}{\log \relax (x) - 3}\right )} + 16 \, x^{2} - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.65, size = 50, normalized size = 1.67 \begin {gather*} -40 \, x^{2} e^{\left (-\frac {\log \relax (5) \log \relax (x)}{\log \relax (x) - 3} + 5\right )} + 25 \, x^{2} e^{\left (-\frac {2 \, \log \relax (5) \log \relax (x)}{\log \relax (x) - 3} + 10\right )} + 16 \, x^{2} - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.64, size = 58, normalized size = 1.93
method | result | size |
risch | \(16 x^{2}-\ln \relax (x )+x^{2} {\mathrm e}^{-\frac {2 \left (-5 \ln \relax (x )+3 \ln \relax (5)+15\right )}{\ln \relax (x )-3}}-8 x^{2} {\mathrm e}^{-\frac {-5 \ln \relax (x )+3 \ln \relax (5)+15}{\ln \relax (x )-3}}\) | \(58\) |
default | \(16 x^{2}-\ln \relax (x )+\frac {24 x^{2} {\mathrm e}^{-\frac {-5 \ln \relax (x )+3 \ln \relax (5)+15}{\ln \relax (x )-3}}-8 \ln \relax (x ) x^{2} {\mathrm e}^{-\frac {-5 \ln \relax (x )+3 \ln \relax (5)+15}{\ln \relax (x )-3}}}{\ln \relax (x )-3}+\frac {\ln \relax (x ) x^{2} {\mathrm e}^{-\frac {2 \left (-5 \ln \relax (x )+3 \ln \relax (5)+15\right )}{\ln \relax (x )-3}}-3 x^{2} {\mathrm e}^{-\frac {2 \left (-5 \ln \relax (x )+3 \ln \relax (5)+15\right )}{\ln \relax (x )-3}}}{\ln \relax (x )-3}\) | \(126\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \frac {16 \, x^{2} \log \relax (x) - 48 \, x^{2} - 9}{\log \relax (x) - 3} + \frac {9}{\log \relax (x) - 3} - \int \frac {8 \, {\left (2 \, x \log \relax (x)^{2} + 3 \, x {\left (\log \relax (5) + 6\right )} - 12 \, x \log \relax (x)\right )} e^{\left (-\frac {3 \, \log \relax (5)}{\log \relax (x) - 3} + \frac {5 \, \log \relax (x)}{\log \relax (x) - 3} - \frac {15}{\log \relax (x) - 3}\right )}}{\log \relax (x)^{2} - 6 \, \log \relax (x) + 9}\,{d x} + \int \frac {2 \, {\left (x \log \relax (x)^{2} + 3 \, x {\left (\log \relax (5) + 3\right )} - 6 \, x \log \relax (x)\right )} e^{\left (-\frac {6 \, \log \relax (5)}{\log \relax (x) - 3} + \frac {10 \, \log \relax (x)}{\log \relax (x) - 3} - \frac {30}{\log \relax (x) - 3}\right )}}{\log \relax (x)^{2} - 6 \, \log \relax (x) + 9}\,{d x} - \log \relax (x) \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 = -0.03 \begin {gather*} \int \frac {{\mathrm {e}}^{-\frac {2\,\left (3\,\ln \relax (5)-5\,\ln \relax (x)+15\right )}{\ln \relax (x)-3}}\,\left (2\,x^2\,{\ln \relax (x)}^2-12\,x^2\,\ln \relax (x)+6\,x^2\,\ln \relax (5)+18\,x^2\right )-{\mathrm {e}}^{-\frac {3\,\ln \relax (5)-5\,\ln \relax (x)+15}{\ln \relax (x)-3}}\,\left (16\,x^2\,{\ln \relax (x)}^2-96\,x^2\,\ln \relax (x)+24\,x^2\,\ln \relax (5)+144\,x^2\right )+{\ln \relax (x)}^2\,\left (32\,x^2-1\right )+288\,x^2-\ln \relax (x)\,\left (192\,x^2-6\right )-9}{x\,{\ln \relax (x)}^2-6\,x\,\ln \relax (x)+9\,x} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 3.14, size = 53, normalized size = 1.77 \begin {gather*} x^{2} e^{\frac {2 \left (5 \log {\relax (x )} - 15 - 3 \log {\relax (5 )}\right )}{\log {\relax (x )} - 3}} - 8 x^{2} e^{\frac {5 \log {\relax (x )} - 15 - 3 \log {\relax (5 )}}{\log {\relax (x )} - 3}} + 16 x^{2} - \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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