Optimal. Leaf size=31 \[ -x+\frac {x}{\log (4)+\frac {2 \left (1+e^5\right )}{x+\log \left (x+\frac {\log (3)}{5}\right )}} \]
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Rubi [F] time = 2.81, 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 {-10 x-20 e^{10} x+20 x^2+e^5 \left (-30 x+20 x^2\right )+\left (-4-4 e^{10}+4 x+e^5 (-8+4 x)\right ) \log (3)+\left (-20 x^2-20 e^5 x^2+5 x^3+\left (-4 x-4 e^5 x+x^2\right ) \log (3)\right ) \log (4)+\left (-5 x^3-x^2 \log (3)\right ) \log ^2(4)+\left (10 x+10 e^5 x+\left (2+2 e^5\right ) \log (3)+\left (-20 x-20 e^5 x+10 x^2+\left (-4-4 e^5+2 x\right ) \log (3)\right ) \log (4)+\left (-10 x^2-2 x \log (3)\right ) \log ^2(4)\right ) \log \left (\frac {1}{5} (5 x+\log (3))\right )+\left ((5 x+\log (3)) \log (4)+(-5 x-\log (3)) \log ^2(4)\right ) \log ^2\left (\frac {1}{5} (5 x+\log (3))\right )}{20 x+40 e^5 x+20 e^{10} x+\left (4+8 e^5+4 e^{10}\right ) \log (3)+\left (20 x^2+20 e^5 x^2+\left (4 x+4 e^5 x\right ) \log (3)\right ) \log (4)+\left (5 x^3+x^2 \log (3)\right ) \log ^2(4)+\left (\left (20 x+20 e^5 x+\left (4+4 e^5\right ) \log (3)\right ) \log (4)+\left (10 x^2+2 x \log (3)\right ) \log ^2(4)\right ) \log \left (\frac {1}{5} (5 x+\log (3))\right )+(5 x+\log (3)) \log ^2(4) \log ^2\left (\frac {1}{5} (5 x+\log (3))\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-10 x-20 e^{10} x+20 x^2+e^5 \left (-30 x+20 x^2\right )+\left (-4-4 e^{10}+4 x+e^5 (-8+4 x)\right ) \log (3)+\left (-20 x^2-20 e^5 x^2+5 x^3+\left (-4 x-4 e^5 x+x^2\right ) \log (3)\right ) \log (4)+\left (-5 x^3-x^2 \log (3)\right ) \log ^2(4)+\left (10 x+10 e^5 x+\left (2+2 e^5\right ) \log (3)+\left (-20 x-20 e^5 x+10 x^2+\left (-4-4 e^5+2 x\right ) \log (3)\right ) \log (4)+\left (-10 x^2-2 x \log (3)\right ) \log ^2(4)\right ) \log \left (\frac {1}{5} (5 x+\log (3))\right )+\left ((5 x+\log (3)) \log (4)+(-5 x-\log (3)) \log ^2(4)\right ) \log ^2\left (\frac {1}{5} (5 x+\log (3))\right )}{20 e^{10} x+\left (20+40 e^5\right ) x+\left (4+8 e^5+4 e^{10}\right ) \log (3)+\left (20 x^2+20 e^5 x^2+\left (4 x+4 e^5 x\right ) \log (3)\right ) \log (4)+\left (5 x^3+x^2 \log (3)\right ) \log ^2(4)+\left (\left (20 x+20 e^5 x+\left (4+4 e^5\right ) \log (3)\right ) \log (4)+\left (10 x^2+2 x \log (3)\right ) \log ^2(4)\right ) \log \left (\frac {1}{5} (5 x+\log (3))\right )+(5 x+\log (3)) \log ^2(4) \log ^2\left (\frac {1}{5} (5 x+\log (3))\right )} \, dx\\ &=\int \frac {-10 x-20 e^{10} x+20 x^2+e^5 \left (-30 x+20 x^2\right )+\left (-4-4 e^{10}+4 x+e^5 (-8+4 x)\right ) \log (3)+\left (-20 x^2-20 e^5 x^2+5 x^3+\left (-4 x-4 e^5 x+x^2\right ) \log (3)\right ) \log (4)+\left (-5 x^3-x^2 \log (3)\right ) \log ^2(4)+\left (10 x+10 e^5 x+\left (2+2 e^5\right ) \log (3)+\left (-20 x-20 e^5 x+10 x^2+\left (-4-4 e^5+2 x\right ) \log (3)\right ) \log (4)+\left (-10 x^2-2 x \log (3)\right ) \log ^2(4)\right ) \log \left (\frac {1}{5} (5 x+\log (3))\right )+\left ((5 x+\log (3)) \log (4)+(-5 x-\log (3)) \log ^2(4)\right ) \log ^2\left (\frac {1}{5} (5 x+\log (3))\right )}{\left (20+40 e^5+20 e^{10}\right ) x+\left (4+8 e^5+4 e^{10}\right ) \log (3)+\left (20 x^2+20 e^5 x^2+\left (4 x+4 e^5 x\right ) \log (3)\right ) \log (4)+\left (5 x^3+x^2 \log (3)\right ) \log ^2(4)+\left (\left (20 x+20 e^5 x+\left (4+4 e^5\right ) \log (3)\right ) \log (4)+\left (10 x^2+2 x \log (3)\right ) \log ^2(4)\right ) \log \left (\frac {1}{5} (5 x+\log (3))\right )+(5 x+\log (3)) \log ^2(4) \log ^2\left (\frac {1}{5} (5 x+\log (3))\right )} \, dx\\ &=\int \frac {\left (-10-20 e^{10}\right ) x+20 x^2+e^5 \left (-30 x+20 x^2\right )+\left (-4-4 e^{10}+4 x+e^5 (-8+4 x)\right ) \log (3)+\left (-20 x^2-20 e^5 x^2+5 x^3+\left (-4 x-4 e^5 x+x^2\right ) \log (3)\right ) \log (4)+\left (-5 x^3-x^2 \log (3)\right ) \log ^2(4)+\left (10 x+10 e^5 x+\left (2+2 e^5\right ) \log (3)+\left (-20 x-20 e^5 x+10 x^2+\left (-4-4 e^5+2 x\right ) \log (3)\right ) \log (4)+\left (-10 x^2-2 x \log (3)\right ) \log ^2(4)\right ) \log \left (\frac {1}{5} (5 x+\log (3))\right )+\left ((5 x+\log (3)) \log (4)+(-5 x-\log (3)) \log ^2(4)\right ) \log ^2\left (\frac {1}{5} (5 x+\log (3))\right )}{\left (20+40 e^5+20 e^{10}\right ) x+\left (4+8 e^5+4 e^{10}\right ) \log (3)+\left (20 x^2+20 e^5 x^2+\left (4 x+4 e^5 x\right ) \log (3)\right ) \log (4)+\left (5 x^3+x^2 \log (3)\right ) \log ^2(4)+\left (\left (20 x+20 e^5 x+\left (4+4 e^5\right ) \log (3)\right ) \log (4)+\left (10 x^2+2 x \log (3)\right ) \log ^2(4)\right ) \log \left (\frac {1}{5} (5 x+\log (3))\right )+(5 x+\log (3)) \log ^2(4) \log ^2\left (\frac {1}{5} (5 x+\log (3))\right )} \, dx\\ &=\int \frac {-4 \left (1+e^5\right )^2 \log (3)-5 x^3 (-1+\log (4)) \log (4)-x^2 (-1+\log (4)) \left (20+20 e^5+\log (3) \log (4)\right )-\left (1+e^5\right ) x \left (10+20 e^5+(-1+\log (4)) \log (81)\right )-2 (5 x+\log (3)) \left (-1+x (-1+\log (4)) \log (4)+e^5 (-1+\log (16))+\log (16)\right ) \log \left (x+\frac {\log (3)}{5}\right )-(5 x+\log (3)) (-1+\log (4)) \log (4) \log ^2\left (x+\frac {\log (3)}{5}\right )}{(5 x+\log (3)) \left (2 \left (1+e^5\right )+x \log (4)+\log (4) \log \left (x+\frac {\log (3)}{5}\right )\right )^2} \, dx\\ &=\int \left (\frac {1-\log (4)}{\log (4)}+\frac {\left (1+e^5\right ) x \left (10 x \log (4)+\log (4) \log (9)+\log (4) \log (9) \log (16)-\log ^2(4) \log (81)+\log (1048576)\right )}{(5 x+\log (3)) \log (4) \left (2 \left (1+e^5\right )+x \log (4)+\log (4) \log \left (x+\frac {\log (3)}{5}\right )\right )^2}+\frac {2 \left (-1-e^5\right )}{\log (4) \left (2 \left (1+e^5\right )+x \log (4)+\log (4) \log \left (x+\frac {\log (3)}{5}\right )\right )}\right ) \, dx\\ &=\frac {x (1-\log (4))}{\log (4)}+\frac {\left (1+e^5\right ) \int \frac {x \left (10 x \log (4)+\log (4) \log (9)+\log (4) \log (9) \log (16)-\log ^2(4) \log (81)+\log (1048576)\right )}{(5 x+\log (3)) \left (2 \left (1+e^5\right )+x \log (4)+\log (4) \log \left (x+\frac {\log (3)}{5}\right )\right )^2} \, dx}{\log (4)}-\frac {\left (2 \left (1+e^5\right )\right ) \int \frac {1}{2 \left (1+e^5\right )+x \log (4)+\log (4) \log \left (x+\frac {\log (3)}{5}\right )} \, dx}{\log (4)}\\ &=\frac {x (1-\log (4))}{\log (4)}+\frac {\left (1+e^5\right ) \int \left (\frac {2 x \log (4)}{\left (2 \left (1+e^5\right )+x \log (4)+\log (4) \log \left (x+\frac {\log (3)}{5}\right )\right )^2}+\frac {\log (3) \left (-\log (4) \log (9) \log (16)+\log ^2(4) \log (81)-\log (1048576)\right )}{5 (5 x+\log (3)) \left (2 \left (1+e^5\right )+x \log (4)+\log (4) \log \left (x+\frac {\log (3)}{5}\right )\right )^2}+\frac {\log (4) \log (9) \log (16)-\log ^2(4) \log (81)+\log (1048576)}{5 \left (2 \left (1+e^5\right )+x \log (4)+\log (4) \log \left (x+\frac {\log (3)}{5}\right )\right )^2}\right ) \, dx}{\log (4)}-\frac {\left (2 \left (1+e^5\right )\right ) \int \frac {1}{2 \left (1+e^5\right )+x \log (4)+\log (4) \log \left (x+\frac {\log (3)}{5}\right )} \, dx}{\log (4)}\\ &=\frac {x (1-\log (4))}{\log (4)}+\left (2 \left (1+e^5\right )\right ) \int \frac {x}{\left (2 \left (1+e^5\right )+x \log (4)+\log (4) \log \left (x+\frac {\log (3)}{5}\right )\right )^2} \, dx-\frac {\left (2 \left (1+e^5\right )\right ) \int \frac {1}{2 \left (1+e^5\right )+x \log (4)+\log (4) \log \left (x+\frac {\log (3)}{5}\right )} \, dx}{\log (4)}+\frac {\left (\left (1+e^5\right ) \left (\log (4) \log (9) \log (16)-\log ^2(4) \log (81)+\log (1048576)\right )\right ) \int \frac {1}{\left (2 \left (1+e^5\right )+x \log (4)+\log (4) \log \left (x+\frac {\log (3)}{5}\right )\right )^2} \, dx}{5 \log (4)}-\frac {\left (\left (1+e^5\right ) \log (3) \left (\log (4) \log (9) \log (16)-\log ^2(4) \log (81)+\log (1048576)\right )\right ) \int \frac {1}{(5 x+\log (3)) \left (2 \left (1+e^5\right )+x \log (4)+\log (4) \log \left (x+\frac {\log (3)}{5}\right )\right )^2} \, dx}{5 \log (4)}\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.22, size = 81, normalized size = 2.61 \begin {gather*} -\frac {x (-1+\log (4)) \log (4)+\frac {\left (1+e^5\right ) x \left (10 x \log (4)+\log (4) \log (9) (1+\log (16))-\log ^2(4) \log (81)+\log (1048576)\right )}{(5+5 x+\log (3)) \left (2+2 e^5+x \log (4)+\log (4) \log \left (x+\frac {\log (3)}{5}\right )\right )}}{\log ^2(4)} \end {gather*}
Warning: Unable to verify antiderivative.
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fricas [B] time = 0.59, size = 60, normalized size = 1.94 \begin {gather*} -\frac {2 \, x^{2} \log \relax (2) - x^{2} + 2 \, x e^{5} + {\left (2 \, x \log \relax (2) - x\right )} \log \left (x + \frac {1}{5} \, \log \relax (3)\right ) + 2 \, x}{2 \, {\left (x \log \relax (2) + \log \relax (2) \log \left (x + \frac {1}{5} \, \log \relax (3)\right ) + e^{5} + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.39, size = 82, normalized size = 2.65 \begin {gather*} -\frac {2 \, x^{2} \log \relax (2) - 2 \, x \log \relax (5) \log \relax (2) + 2 \, x \log \relax (2) \log \left (5 \, x + \log \relax (3)\right ) - x^{2} + 2 \, x e^{5} + x \log \relax (5) - x \log \left (5 \, x + \log \relax (3)\right ) + 2 \, x}{2 \, {\left (x \log \relax (2) - \log \relax (5) \log \relax (2) + \log \relax (2) \log \left (5 \, x + \log \relax (3)\right ) + e^{5} + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.45, size = 43, normalized size = 1.39
method | result | size |
risch | \(-x +\frac {x}{2 \ln \relax (2)}-\frac {\left ({\mathrm e}^{5}+1\right ) x}{2 \ln \relax (2) \left (\ln \relax (2) \ln \left (\frac {\ln \relax (3)}{5}+x \right )+x \ln \relax (2)+{\mathrm e}^{5}+1\right )}\) | \(43\) |
norman | \(\frac {\left (-\ln \relax (2)+\frac {1}{2}\right ) x^{2}+\left ({\mathrm e}^{5}+1\right ) \ln \left (\frac {\ln \relax (3)}{5}+x \right )+\left (-\ln \relax (2)+\frac {1}{2}\right ) x \ln \left (\frac {\ln \relax (3)}{5}+x \right )+\frac {{\mathrm e}^{10}+2 \,{\mathrm e}^{5}+1}{\ln \relax (2)}}{\ln \relax (2) \ln \left (\frac {\ln \relax (3)}{5}+x \right )+x \ln \relax (2)+{\mathrm e}^{5}+1}\) | \(75\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.55, size = 73, normalized size = 2.35 \begin {gather*} -\frac {x^{2} {\left (2 \, \log \relax (2) - 1\right )} + x {\left (2 \, \log \relax (2) - 1\right )} \log \left (5 \, x + \log \relax (3)\right ) - {\left (2 \, \log \relax (5) \log \relax (2) - 2 \, e^{5} - \log \relax (5) - 2\right )} x}{2 \, {\left (x \log \relax (2) - \log \relax (5) \log \relax (2) + \log \relax (2) \log \left (5 \, x + \log \relax (3)\right ) + e^{5} + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.55, size = 126, normalized size = 4.06 \begin {gather*} \frac {2\,{\mathrm {e}}^5+{\mathrm {e}}^{10}+x^2\,{\ln \relax (2)}^2-2\,x^2\,{\ln \relax (2)}^3+x\,\ln \relax (2)-2\,x\,{\ln \relax (2)}^2+\ln \left (x+\frac {\ln \relax (3)}{5}\right )\,\ln \relax (2)-2\,x\,{\mathrm {e}}^5\,{\ln \relax (2)}^2+\ln \left (x+\frac {\ln \relax (3)}{5}\right )\,{\mathrm {e}}^5\,\ln \relax (2)+x\,{\mathrm {e}}^5\,\ln \relax (2)+x\,\ln \left (x+\frac {\ln \relax (3)}{5}\right )\,{\ln \relax (2)}^2-2\,x\,\ln \left (x+\frac {\ln \relax (3)}{5}\right )\,{\ln \relax (2)}^3+1}{2\,{\ln \relax (2)}^2\,\left ({\mathrm {e}}^5+x\,\ln \relax (2)+\ln \left (x+\frac {\ln \relax (3)}{5}\right )\,\ln \relax (2)+1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.37, size = 58, normalized size = 1.87 \begin {gather*} \frac {x \left (1 - 2 \log {\relax (2 )}\right )}{2 \log {\relax (2 )}} + \frac {- x e^{5} - x}{2 x \log {\relax (2 )}^{2} + 2 \log {\relax (2 )}^{2} \log {\left (x + \frac {\log {\relax (3 )}}{5} \right )} + 2 \log {\relax (2 )} + 2 e^{5} \log {\relax (2 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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