Optimal. Leaf size=29 \[ \log \left (\left (\frac {13}{4}+e^{2 x+\left (-7+\frac {5}{x}-\log (2)\right )^2}-x\right )^2\right ) \]
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Rubi [F] time = 8.25, 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 {-8 x^3+\exp \left (\frac {25-70 x+49 x^2+2 x^3+\left (-10 x+14 x^2\right ) \log (2)+x^2 \log ^2(2)}{x^2}\right ) \left (-400+560 x+16 x^3+80 x \log (2)\right )}{13 x^3+4 \exp \left (\frac {25-70 x+49 x^2+2 x^3+\left (-10 x+14 x^2\right ) \log (2)+x^2 \log ^2(2)}{x^2}\right ) x^3-4 x^4} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {4 \left (-25+x^3+5 x (7+\log (2))\right )}{x^3}+\frac {2^{2+\frac {10}{x}} e^{70/x} \left (325-15 x^3+4 x^4+20 x^2 (7+\log (2))-5 x (111+\log (8192))\right )}{x^3 \left (13\ 2^{10/x} e^{70/x}+65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}-2^{2+\frac {10}{x}} e^{70/x} x\right )}\right ) \, dx\\ &=4 \int \frac {-25+x^3+5 x (7+\log (2))}{x^3} \, dx+\int \frac {2^{2+\frac {10}{x}} e^{70/x} \left (325-15 x^3+4 x^4+20 x^2 (7+\log (2))-5 x (111+\log (8192))\right )}{x^3 \left (13\ 2^{10/x} e^{70/x}+65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}-2^{2+\frac {10}{x}} e^{70/x} x\right )} \, dx\\ &=4 \int \left (1-\frac {25}{x^3}+\frac {5 (7+\log (2))}{x^2}\right ) \, dx+\int \frac {4 e^{\frac {70+10 \log (2)}{x}} \left (325-15 x^3+4 x^4+20 x^2 (7+\log (2))-5 x (111+\log (8192))\right )}{x^3 \left (13\ 2^{10/x} e^{70/x}+65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}-2^{2+\frac {10}{x}} e^{70/x} x\right )} \, dx\\ &=\frac {50}{x^2}+4 x-\frac {20 (7+\log (2))}{x}+4 \int \frac {e^{\frac {70+10 \log (2)}{x}} \left (325-15 x^3+4 x^4+20 x^2 (7+\log (2))-5 x (111+\log (8192))\right )}{x^3 \left (13\ 2^{10/x} e^{70/x}+65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}-2^{2+\frac {10}{x}} e^{70/x} x\right )} \, dx\\ &=\frac {50}{x^2}+4 x-\frac {20 (7+\log (2))}{x}+4 \int \left (\frac {15 e^{\frac {70+10 \log (2)}{x}}}{-13 4^{5/x} e^{70/x}-65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}+4^{1+\frac {5}{x}} e^{70/x} x}-\frac {325 e^{\frac {70+10 \log (2)}{x}}}{x^3 \left (-13 4^{5/x} e^{70/x}-65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}+4^{1+\frac {5}{x}} e^{70/x} x\right )}-\frac {4 e^{\frac {70+10 \log (2)}{x}} x}{-13 4^{5/x} e^{70/x}-65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}+4^{1+\frac {5}{x}} e^{70/x} x}-\frac {20 e^{\frac {70+10 \log (2)}{x}} (7+\log (2))}{x \left (-13 4^{5/x} e^{70/x}-65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}+4^{1+\frac {5}{x}} e^{70/x} x\right )}+\frac {5 e^{\frac {70+10 \log (2)}{x}} (111+\log (8192))}{x^2 \left (-13 4^{5/x} e^{70/x}-65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}+4^{1+\frac {5}{x}} e^{70/x} x\right )}\right ) \, dx\\ &=\frac {50}{x^2}+4 x-\frac {20 (7+\log (2))}{x}-16 \int \frac {e^{\frac {70+10 \log (2)}{x}} x}{-13 4^{5/x} e^{70/x}-65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}+4^{1+\frac {5}{x}} e^{70/x} x} \, dx+60 \int \frac {e^{\frac {70+10 \log (2)}{x}}}{-13 4^{5/x} e^{70/x}-65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}+4^{1+\frac {5}{x}} e^{70/x} x} \, dx-1300 \int \frac {e^{\frac {70+10 \log (2)}{x}}}{x^3 \left (-13 4^{5/x} e^{70/x}-65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}+4^{1+\frac {5}{x}} e^{70/x} x\right )} \, dx-(80 (7+\log (2))) \int \frac {e^{\frac {70+10 \log (2)}{x}}}{x \left (-13 4^{5/x} e^{70/x}-65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}+4^{1+\frac {5}{x}} e^{70/x} x\right )} \, dx+(20 (111+\log (8192))) \int \frac {e^{\frac {70+10 \log (2)}{x}}}{x^2 \left (-13 4^{5/x} e^{70/x}-65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}+4^{1+\frac {5}{x}} e^{70/x} x\right )} \, dx\\ &=\frac {50}{x^2}+4 x-\frac {20 (7+\log (2))}{x}-16 \int \frac {e^{\frac {70+10 \log (2)}{x}} x}{-13 4^{5/x} e^{70/x}-65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}+4^{1+\frac {5}{x}} e^{70/x} x} \, dx+60 \int \frac {e^{\frac {70+10 \log (2)}{x}}}{-13 4^{5/x} e^{70/x}-65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}+4^{1+\frac {5}{x}} e^{70/x} x} \, dx-1300 \int \frac {e^{\frac {70+10 \log (2)}{x}}}{x^3 \left (-13 4^{5/x} e^{70/x}-65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}+4^{1+\frac {5}{x}} e^{70/x} x\right )} \, dx+\frac {(80 (7+\log (2))) \operatorname {Subst}\left (\int \frac {\exp \left (-\frac {4^{1+\frac {5}{x}} e^{70/x} (70+10 \log (2))}{-13 4^{5/x} e^{70/x}-65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}}+\frac {x (70+10 \log (2))}{-13 4^{5/x} e^{70/x}-65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}}\right )}{x} \, dx,x,\frac {-13 4^{5/x} e^{70/x}-65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}+4^{1+\frac {5}{x}} e^{70/x} x}{x}\right )}{-13 4^{5/x} e^{70/x}-65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}}+(20 (111+\log (8192))) \int \frac {e^{\frac {70+10 \log (2)}{x}}}{x^2 \left (-13 4^{5/x} e^{70/x}-65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}+4^{1+\frac {5}{x}} e^{70/x} x\right )} \, dx\\ &=\frac {50}{x^2}+4 x-\frac {20 (7+\log (2))}{x}-16 \int \frac {e^{\frac {70+10 \log (2)}{x}} x}{-13 4^{5/x} e^{70/x}-65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}+4^{1+\frac {5}{x}} e^{70/x} x} \, dx+60 \int \frac {e^{\frac {70+10 \log (2)}{x}}}{-13 4^{5/x} e^{70/x}-65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}+4^{1+\frac {5}{x}} e^{70/x} x} \, dx-1300 \int \frac {e^{\frac {70+10 \log (2)}{x}}}{x^3 \left (-13 4^{5/x} e^{70/x}-65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}+4^{1+\frac {5}{x}} e^{70/x} x\right )} \, dx+\frac {(80 (7+\log (2))) \operatorname {Subst}\left (\int \frac {\exp \left (\frac {10 \left (4^{\frac {5+x}{x}} e^{70/x}-x\right ) (7+\log (2))}{13\ 4^{5/x} e^{70/x}+65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}}\right )}{x} \, dx,x,\frac {-13 4^{5/x} e^{70/x}-65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}+4^{1+\frac {5}{x}} e^{70/x} x}{x}\right )}{-13 4^{5/x} e^{70/x}-65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}}+(20 (111+\log (8192))) \int \frac {e^{\frac {70+10 \log (2)}{x}}}{x^2 \left (-13 4^{5/x} e^{70/x}-65536 e^{49+\frac {25}{x^2}+2 x+\log ^2(2)}+4^{1+\frac {5}{x}} e^{70/x} x\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [F] time = 0.65, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {-8 x^3+e^{\frac {25-70 x+49 x^2+2 x^3+\left (-10 x+14 x^2\right ) \log (2)+x^2 \log ^2(2)}{x^2}} \left (-400+560 x+16 x^3+80 x \log (2)\right )}{13 x^3+4 e^{\frac {25-70 x+49 x^2+2 x^3+\left (-10 x+14 x^2\right ) \log (2)+x^2 \log ^2(2)}{x^2}} x^3-4 x^4} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.58, size = 51, normalized size = 1.76 \begin {gather*} 2 \, \log \left (-4 \, x + 4 \, e^{\left (\frac {x^{2} \log \relax (2)^{2} + 2 \, x^{3} + 49 \, x^{2} + 2 \, {\left (7 \, x^{2} - 5 \, x\right )} \log \relax (2) - 70 \, x + 25}{x^{2}}\right )} + 13\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.37, size = 50, normalized size = 1.72 \begin {gather*} 2 \, \log \left (4 \, x - 4 \, e^{\left (\frac {x^{2} \log \relax (2)^{2} + 2 \, x^{3} + 14 \, x^{2} \log \relax (2) + 49 \, x^{2} - 10 \, x \log \relax (2) - 70 \, x + 25}{x^{2}}\right )} - 13\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.23, size = 51, normalized size = 1.76
method | result | size |
norman | \(2 \ln \left (4 x -4 \,{\mathrm e}^{\frac {x^{2} \ln \relax (2)^{2}+\left (14 x^{2}-10 x \right ) \ln \relax (2)+2 x^{3}+49 x^{2}-70 x +25}{x^{2}}}-13\right )\) | \(51\) |
risch | \(4 x +\frac {\left (-20 \ln \relax (2)-140\right ) x +50}{x^{2}}-\frac {2 \left (x^{2} \ln \relax (2)^{2}+\left (14 x^{2}-10 x \right ) \ln \relax (2)+2 x^{3}+49 x^{2}-70 x +25\right )}{x^{2}}+2 \ln \left (-x +16384 \left (\frac {1}{1024}\right )^{\frac {1}{x}} {\mathrm e}^{\frac {x^{2} \ln \relax (2)^{2}+2 x^{3}+49 x^{2}-70 x +25}{x^{2}}}+\frac {13}{4}\right )\) | \(102\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.91, size = 71, normalized size = 2.45 \begin {gather*} -\frac {20 \, \log \relax (2)}{x} + 2 \, \log \left (4 \, x - 13\right ) + 2 \, \log \left (\frac {{\left ({\left (4 \, x - 13\right )} e^{\left (\frac {10 \, \log \relax (2)}{x} + \frac {70}{x}\right )} - 65536 \, e^{\left (\log \relax (2)^{2} + 2 \, x + \frac {25}{x^{2}} + 49\right )}\right )} e^{\left (-\frac {70}{x}\right )}}{4 \, x - 13}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.94, size = 56, normalized size = 1.93 \begin {gather*} 2\,\ln \left (13\,2^{10/x}-4\,2^{10/x}\,x+65536\,{\mathrm {e}}^{{\ln \relax (2)}^2}\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{49}\,{\mathrm {e}}^{\frac {25}{x^2}}\,{\mathrm {e}}^{-\frac {70}{x}}\right )-\frac {20\,\ln \relax (2)}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.34, size = 48, normalized size = 1.66 \begin {gather*} 2 \log {\left (- x + e^{\frac {2 x^{3} + x^{2} \log {\relax (2 )}^{2} + 49 x^{2} - 70 x + \left (14 x^{2} - 10 x\right ) \log {\relax (2 )} + 25}{x^{2}}} + \frac {13}{4} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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