Optimal. Leaf size=22 \[ \log \left (\left (x+2 e \left (3+x+16 x^2-\log (4)\right )^4\right )^2\right ) \]
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Rubi [B] time = 0.13, antiderivative size = 132, normalized size of antiderivative = 6.00, number of steps used = 1, number of rules used = 1, integrand size = 230, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.004, Rules used = {1587} \begin {gather*} 2 \log \left (-8 e \left (16 x^2+x+3\right ) \log ^3(4)+12 e \left (256 x^4+32 x^3+97 x^2+6 x+9\right ) \log ^2(4)-8 e \left (4096 x^6+768 x^5+2352 x^4+289 x^3+441 x^2+27 x+27\right ) \log (4)+2 e \left (65536 x^8+16384 x^7+50688 x^6+9280 x^5+14401 x^4+1740 x^3+1782 x^2+108 x+81\right )+x+2 e \log ^4(4)\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 1587
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 \log \left (x+2 e \left (81+108 x+1782 x^2+1740 x^3+14401 x^4+9280 x^5+50688 x^6+16384 x^7+65536 x^8\right )-8 e \left (27+27 x+441 x^2+289 x^3+2352 x^4+768 x^5+4096 x^6\right ) \log (4)+12 e \left (9+6 x+97 x^2+32 x^3+256 x^4\right ) \log ^2(4)-8 e \left (3+x+16 x^2\right ) \log ^3(4)+2 e \log ^4(4)\right )\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.14, size = 182, normalized size = 8.27 \begin {gather*} 2 \log \left (162 e+x+216 e x+3564 e x^2+3480 e x^3+28802 e x^4+18560 e x^5+101376 e x^6+32768 e x^7+131072 e x^8-216 e \log (4)-216 e x \log (4)-3528 e x^2 \log (4)-2312 e x^3 \log (4)-18816 e x^4 \log (4)-6144 e x^5 \log (4)-32768 e x^6 \log (4)+108 e \log ^2(4)+72 e x \log ^2(4)+1164 e x^2 \log ^2(4)+384 e x^3 \log ^2(4)+3072 e x^4 \log ^2(4)-24 e \log ^3(4)-8 e x \log ^3(4)-128 e x^2 \log ^3(4)+2 e \log ^4(4)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 1.08, size = 137, normalized size = 6.23 \begin {gather*} 2 \, \log \left (-64 \, {\left (16 \, x^{2} + x + 3\right )} e \log \relax (2)^{3} + 32 \, e \log \relax (2)^{4} + 48 \, {\left (256 \, x^{4} + 32 \, x^{3} + 97 \, x^{2} + 6 \, x + 9\right )} e \log \relax (2)^{2} - 16 \, {\left (4096 \, x^{6} + 768 \, x^{5} + 2352 \, x^{4} + 289 \, x^{3} + 441 \, x^{2} + 27 \, x + 27\right )} e \log \relax (2) + 2 \, {\left (65536 \, x^{8} + 16384 \, x^{7} + 50688 \, x^{6} + 9280 \, x^{5} + 14401 \, x^{4} + 1740 \, x^{3} + 1782 \, x^{2} + 108 \, x + 81\right )} e + x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.19, size = 159, normalized size = 7.23 \begin {gather*} 2 \, \log \left (-64 \, {\left (16 \, x^{2} + x\right )} e \log \relax (2)^{3} + 32 \, e \log \relax (2)^{4} + 48 \, {\left (256 \, x^{4} + 32 \, x^{3} + 97 \, x^{2} + 6 \, x\right )} e \log \relax (2)^{2} - 192 \, e \log \relax (2)^{3} - 16 \, {\left (4096 \, x^{6} + 768 \, x^{5} + 2352 \, x^{4} + 289 \, x^{3} + 441 \, x^{2} + 27 \, x\right )} e \log \relax (2) + 432 \, e \log \relax (2)^{2} + 2 \, {\left (65536 \, x^{8} + 16384 \, x^{7} + 50688 \, x^{6} + 9280 \, x^{5} + 14401 \, x^{4} + 1740 \, x^{3} + 1782 \, x^{2} + 108 \, x\right )} e - 432 \, e \log \relax (2) + x + 162 \, e\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.19, size = 190, normalized size = 8.64
method | result | size |
risch | \(2 \ln \left (131072 x^{8} {\mathrm e}+32768 x^{7} {\mathrm e}+\left (-65536 \,{\mathrm e} \ln \relax (2)+101376 \,{\mathrm e}\right ) x^{6}+\left (-12288 \,{\mathrm e} \ln \relax (2)+18560 \,{\mathrm e}\right ) x^{5}+\left (12288 \,{\mathrm e} \ln \relax (2)^{2}-37632 \,{\mathrm e} \ln \relax (2)+28802 \,{\mathrm e}\right ) x^{4}+\left (1536 \,{\mathrm e} \ln \relax (2)^{2}-4624 \,{\mathrm e} \ln \relax (2)+3480 \,{\mathrm e}\right ) x^{3}+\left (-1024 \,{\mathrm e} \ln \relax (2)^{3}+4656 \,{\mathrm e} \ln \relax (2)^{2}-7056 \,{\mathrm e} \ln \relax (2)+3564 \,{\mathrm e}\right ) x^{2}+\left (-64 \,{\mathrm e} \ln \relax (2)^{3}+288 \,{\mathrm e} \ln \relax (2)^{2}-432 \,{\mathrm e} \ln \relax (2)+216 \,{\mathrm e}+1\right ) x +32 \,{\mathrm e} \ln \relax (2)^{4}-192 \,{\mathrm e} \ln \relax (2)^{3}+432 \,{\mathrm e} \ln \relax (2)^{2}-432 \,{\mathrm e} \ln \relax (2)+162 \,{\mathrm e}\right )\) | \(190\) |
default | \(2 \ln \left (-432 x \,{\mathrm e} \ln \relax (2)+x +4656 x^{2} {\mathrm e} \ln \relax (2)^{2}+131072 x^{8} {\mathrm e}+32 \,{\mathrm e} \ln \relax (2)^{4}+32768 x^{7} {\mathrm e}+162 \,{\mathrm e}+288 \ln \relax (2)^{2} {\mathrm e} x +18560 x^{5} {\mathrm e}-432 \,{\mathrm e} \ln \relax (2)+432 \,{\mathrm e} \ln \relax (2)^{2}-65536 \,{\mathrm e} \ln \relax (2) x^{6}+12288 \,{\mathrm e} \ln \relax (2)^{2} x^{4}-12288 \,{\mathrm e} \ln \relax (2) x^{5}-1024 \,{\mathrm e} \ln \relax (2)^{3} x^{2}+1536 \,{\mathrm e} \ln \relax (2)^{2} x^{3}-37632 \,{\mathrm e} \ln \relax (2) x^{4}-64 \,{\mathrm e} \ln \relax (2)^{3} x -4624 \,{\mathrm e} \ln \relax (2) x^{3}-7056 \,{\mathrm e} \ln \relax (2) x^{2}+28802 x^{4} {\mathrm e}+216 x \,{\mathrm e}+3564 x^{2} {\mathrm e}+3480 x^{3} {\mathrm e}-192 \,{\mathrm e} \ln \relax (2)^{3}+101376 x^{6} {\mathrm e}\right )\) | \(208\) |
norman | \(2 \ln \left (-432 x \,{\mathrm e} \ln \relax (2)+x +4656 x^{2} {\mathrm e} \ln \relax (2)^{2}+131072 x^{8} {\mathrm e}+32 \,{\mathrm e} \ln \relax (2)^{4}+32768 x^{7} {\mathrm e}+162 \,{\mathrm e}+288 \ln \relax (2)^{2} {\mathrm e} x +18560 x^{5} {\mathrm e}-432 \,{\mathrm e} \ln \relax (2)+432 \,{\mathrm e} \ln \relax (2)^{2}-65536 \,{\mathrm e} \ln \relax (2) x^{6}+12288 \,{\mathrm e} \ln \relax (2)^{2} x^{4}-12288 \,{\mathrm e} \ln \relax (2) x^{5}-1024 \,{\mathrm e} \ln \relax (2)^{3} x^{2}+1536 \,{\mathrm e} \ln \relax (2)^{2} x^{3}-37632 \,{\mathrm e} \ln \relax (2) x^{4}-64 \,{\mathrm e} \ln \relax (2)^{3} x -4624 \,{\mathrm e} \ln \relax (2) x^{3}-7056 \,{\mathrm e} \ln \relax (2) x^{2}+28802 x^{4} {\mathrm e}+216 x \,{\mathrm e}+3564 x^{2} {\mathrm e}+3480 x^{3} {\mathrm e}-192 \,{\mathrm e} \ln \relax (2)^{3}+101376 x^{6} {\mathrm e}\right )\) | \(208\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.37, size = 195, normalized size = 8.86 \begin {gather*} 2 \, \log \left (131072 \, x^{8} e + 32768 \, x^{7} e - 1024 \, {\left (64 \, e \log \relax (2) - 99 \, e\right )} x^{6} - 128 \, {\left (96 \, e \log \relax (2) - 145 \, e\right )} x^{5} + 2 \, {\left (6144 \, e \log \relax (2)^{2} - 18816 \, e \log \relax (2) + 14401 \, e\right )} x^{4} + 32 \, e \log \relax (2)^{4} + 8 \, {\left (192 \, e \log \relax (2)^{2} - 578 \, e \log \relax (2) + 435 \, e\right )} x^{3} - 192 \, e \log \relax (2)^{3} - 4 \, {\left (256 \, e \log \relax (2)^{3} - 1164 \, e \log \relax (2)^{2} + 1764 \, e \log \relax (2) - 891 \, e\right )} x^{2} + 432 \, e \log \relax (2)^{2} - {\left (64 \, e \log \relax (2)^{3} - 288 \, e \log \relax (2)^{2} + 432 \, e \log \relax (2) - 216 \, e - 1\right )} x - 432 \, e \log \relax (2) + 162 \, e\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F(-1)] time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \text {Hanged} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 3.89, size = 226, normalized size = 10.27 \begin {gather*} 2 \log {\left (131072 e x^{8} + 32768 e x^{7} + x^{6} \left (- 65536 e \log {\relax (2 )} + 101376 e\right ) + x^{5} \left (- 12288 e \log {\relax (2 )} + 18560 e\right ) + x^{4} \left (- 37632 e \log {\relax (2 )} + 12288 e \log {\relax (2 )}^{2} + 28802 e\right ) + x^{3} \left (- 4624 e \log {\relax (2 )} + 1536 e \log {\relax (2 )}^{2} + 3480 e\right ) + x^{2} \left (- 7056 e \log {\relax (2 )} - 1024 e \log {\relax (2 )}^{3} + 4656 e \log {\relax (2 )}^{2} + 3564 e\right ) + x \left (- 432 e \log {\relax (2 )} - 64 e \log {\relax (2 )}^{3} + 1 + 288 e \log {\relax (2 )}^{2} + 216 e\right ) - 432 e \log {\relax (2 )} - 192 e \log {\relax (2 )}^{3} + 32 e \log {\relax (2 )}^{4} + 162 e + 432 e \log {\relax (2 )}^{2} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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