Optimal. Leaf size=23 \[ 2 \left (-x+\frac {3 e^4}{x (3+2 x+\log (x))^4}\right ) \]
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Rubi [F] time = 1.63, 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 {e^4 (-42-60 x)-486 x^2-1620 x^3-2160 x^4-1440 x^5-480 x^6-64 x^7+\left (-6 e^4-810 x^2-2160 x^3-2160 x^4-960 x^5-160 x^6\right ) \log (x)+\left (-540 x^2-1080 x^3-720 x^4-160 x^5\right ) \log ^2(x)+\left (-180 x^2-240 x^3-80 x^4\right ) \log ^3(x)+\left (-30 x^2-20 x^3\right ) \log ^4(x)-2 x^2 \log ^5(x)}{243 x^2+810 x^3+1080 x^4+720 x^5+240 x^6+32 x^7+\left (405 x^2+1080 x^3+1080 x^4+480 x^5+80 x^6\right ) \log (x)+\left (270 x^2+540 x^3+360 x^4+80 x^5\right ) \log ^2(x)+\left (90 x^2+120 x^3+40 x^4\right ) \log ^3(x)+\left (15 x^2+10 x^3\right ) \log ^4(x)+x^2 \log ^5(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 {2 \left (-x^2 (3+2 x)^5-3 e^4 (7+10 x)-\left (3 e^4+5 x^2 (3+2 x)^4\right ) \log (x)-10 x^2 (3+2 x)^3 \log ^2(x)-10 x^2 (3+2 x)^2 \log ^3(x)-5 x^2 (3+2 x) \log ^4(x)-x^2 \log ^5(x)\right )}{x^2 (3+2 x+\log (x))^5} \, dx\\ &=2 \int \frac {-x^2 (3+2 x)^5-3 e^4 (7+10 x)-\left (3 e^4+5 x^2 (3+2 x)^4\right ) \log (x)-10 x^2 (3+2 x)^3 \log ^2(x)-10 x^2 (3+2 x)^2 \log ^3(x)-5 x^2 (3+2 x) \log ^4(x)-x^2 \log ^5(x)}{x^2 (3+2 x+\log (x))^5} \, dx\\ &=2 \int \left (-1-\frac {12 e^4 (1+2 x)}{x^2 (3+2 x+\log (x))^5}-\frac {3 e^4}{x^2 (3+2 x+\log (x))^4}\right ) \, dx\\ &=-2 x-\left (6 e^4\right ) \int \frac {1}{x^2 (3+2 x+\log (x))^4} \, dx-\left (24 e^4\right ) \int \frac {1+2 x}{x^2 (3+2 x+\log (x))^5} \, dx\\ &=-2 x-\left (6 e^4\right ) \int \frac {1}{x^2 (3+2 x+\log (x))^4} \, dx-\left (24 e^4\right ) \int \left (\frac {1}{x^2 (3+2 x+\log (x))^5}+\frac {2}{x (3+2 x+\log (x))^5}\right ) \, dx\\ &=-2 x-\left (6 e^4\right ) \int \frac {1}{x^2 (3+2 x+\log (x))^4} \, dx-\left (24 e^4\right ) \int \frac {1}{x^2 (3+2 x+\log (x))^5} \, dx-\left (48 e^4\right ) \int \frac {1}{x (3+2 x+\log (x))^5} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.10, size = 21, normalized size = 0.91 \begin {gather*} -2 \left (x-\frac {3 e^4}{x (3+2 x+\log (x))^4}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.65, size = 194, normalized size = 8.43 \begin {gather*} -\frac {2 \, {\left (16 \, x^{6} + x^{2} \log \relax (x)^{4} + 96 \, x^{5} + 216 \, x^{4} + 4 \, {\left (2 \, x^{3} + 3 \, x^{2}\right )} \log \relax (x)^{3} + 216 \, x^{3} + 6 \, {\left (4 \, x^{4} + 12 \, x^{3} + 9 \, x^{2}\right )} \log \relax (x)^{2} + 81 \, x^{2} + 4 \, {\left (8 \, x^{5} + 36 \, x^{4} + 54 \, x^{3} + 27 \, x^{2}\right )} \log \relax (x) - 3 \, e^{4}\right )}}{16 \, x^{5} + x \log \relax (x)^{4} + 96 \, x^{4} + 4 \, {\left (2 \, x^{2} + 3 \, x\right )} \log \relax (x)^{3} + 216 \, x^{3} + 6 \, {\left (4 \, x^{3} + 12 \, x^{2} + 9 \, x\right )} \log \relax (x)^{2} + 216 \, x^{2} + 4 \, {\left (8 \, x^{4} + 36 \, x^{3} + 54 \, x^{2} + 27 \, x\right )} \log \relax (x) + 81 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.32, size = 212, normalized size = 9.22 \begin {gather*} -\frac {2 \, {\left (16 \, x^{6} + 32 \, x^{5} \log \relax (x) + 24 \, x^{4} \log \relax (x)^{2} + 8 \, x^{3} \log \relax (x)^{3} + x^{2} \log \relax (x)^{4} + 96 \, x^{5} + 144 \, x^{4} \log \relax (x) + 72 \, x^{3} \log \relax (x)^{2} + 12 \, x^{2} \log \relax (x)^{3} + 216 \, x^{4} + 216 \, x^{3} \log \relax (x) + 54 \, x^{2} \log \relax (x)^{2} + 216 \, x^{3} + 108 \, x^{2} \log \relax (x) + 81 \, x^{2} - 3 \, e^{4}\right )}}{16 \, x^{5} + 32 \, x^{4} \log \relax (x) + 24 \, x^{3} \log \relax (x)^{2} + 8 \, x^{2} \log \relax (x)^{3} + x \log \relax (x)^{4} + 96 \, x^{4} + 144 \, x^{3} \log \relax (x) + 72 \, x^{2} \log \relax (x)^{2} + 12 \, x \log \relax (x)^{3} + 216 \, x^{3} + 216 \, x^{2} \log \relax (x) + 54 \, x \log \relax (x)^{2} + 216 \, x^{2} + 108 \, x \log \relax (x) + 81 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 21, normalized size = 0.91
method | result | size |
risch | \(\frac {6 \,{\mathrm e}^{4}}{x \left (\ln \relax (x )+3+2 x \right )^{4}}-2 x\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.44, size = 194, normalized size = 8.43 \begin {gather*} -\frac {2 \, {\left (16 \, x^{6} + x^{2} \log \relax (x)^{4} + 96 \, x^{5} + 216 \, x^{4} + 4 \, {\left (2 \, x^{3} + 3 \, x^{2}\right )} \log \relax (x)^{3} + 216 \, x^{3} + 6 \, {\left (4 \, x^{4} + 12 \, x^{3} + 9 \, x^{2}\right )} \log \relax (x)^{2} + 81 \, x^{2} + 4 \, {\left (8 \, x^{5} + 36 \, x^{4} + 54 \, x^{3} + 27 \, x^{2}\right )} \log \relax (x) - 3 \, e^{4}\right )}}{16 \, x^{5} + x \log \relax (x)^{4} + 96 \, x^{4} + 4 \, {\left (2 \, x^{2} + 3 \, x\right )} \log \relax (x)^{3} + 216 \, x^{3} + 6 \, {\left (4 \, x^{3} + 12 \, x^{2} + 9 \, x\right )} \log \relax (x)^{2} + 216 \, x^{2} + 4 \, {\left (8 \, x^{4} + 36 \, x^{3} + 54 \, x^{2} + 27 \, x\right )} \log \relax (x) + 81 \, 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 = -0.04 \begin {gather*} \int -\frac {{\ln \relax (x)}^4\,\left (20\,x^3+30\,x^2\right )+\ln \relax (x)\,\left (160\,x^6+960\,x^5+2160\,x^4+2160\,x^3+810\,x^2+6\,{\mathrm {e}}^4\right )+2\,x^2\,{\ln \relax (x)}^5+{\ln \relax (x)}^3\,\left (80\,x^4+240\,x^3+180\,x^2\right )+486\,x^2+1620\,x^3+2160\,x^4+1440\,x^5+480\,x^6+64\,x^7+{\ln \relax (x)}^2\,\left (160\,x^5+720\,x^4+1080\,x^3+540\,x^2\right )+{\mathrm {e}}^4\,\left (60\,x+42\right )}{{\ln \relax (x)}^4\,\left (10\,x^3+15\,x^2\right )+x^2\,{\ln \relax (x)}^5+{\ln \relax (x)}^3\,\left (40\,x^4+120\,x^3+90\,x^2\right )+\ln \relax (x)\,\left (80\,x^6+480\,x^5+1080\,x^4+1080\,x^3+405\,x^2\right )+243\,x^2+810\,x^3+1080\,x^4+720\,x^5+240\,x^6+32\,x^7+{\ln \relax (x)}^2\,\left (80\,x^5+360\,x^4+540\,x^3+270\,x^2\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.37, size = 92, normalized size = 4.00 \begin {gather*} - 2 x + \frac {6 e^{4}}{16 x^{5} + 96 x^{4} + 216 x^{3} + 216 x^{2} + x \log {\relax (x )}^{4} + 81 x + \left (8 x^{2} + 12 x\right ) \log {\relax (x )}^{3} + \left (24 x^{3} + 72 x^{2} + 54 x\right ) \log {\relax (x )}^{2} + \left (32 x^{4} + 144 x^{3} + 216 x^{2} + 108 x\right ) \log {\relax (x )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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