Optimal. Leaf size=24 \[ \log \left (-\frac {8}{3}+\left (-5+\frac {3 \log (x)}{x (5+x \log (2))}\right )^4\right ) \]
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Rubi [F]
time = 57.89, 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 {-2812500 x^3-2250000 x^4 \log (2)-675000 x^5 \log ^2(2)-90000 x^6 \log ^3(2)-4500 x^7 \log ^4(2)+\left (1012500 x^2+2812500 x^3+\left (607500 x^3+2812500 x^4\right ) \log (2)+\left (121500 x^4+1012500 x^5\right ) \log ^2(2)+\left (8100 x^5+157500 x^6\right ) \log ^3(2)+9000 x^7 \log ^4(2)\right ) \log (x)+\left (-121500 x-1012500 x^2+\left (-48600 x^2-810000 x^3\right ) \log (2)+\left (-4860 x^3-202500 x^4\right ) \log ^2(2)-16200 x^5 \log ^3(2)\right ) \log ^2(x)+\left (4860+121500 x+\left (972 x+72900 x^2\right ) \log (2)+9720 x^3 \log ^2(2)\right ) \log ^3(x)+(-4860-1944 x \log (2)) \log ^4(x)}{5834375 x^5+5834375 x^6 \log (2)+2333750 x^7 \log ^2(2)+466750 x^8 \log ^3(2)+46675 x^9 \log ^4(2)+1867 x^{10} \log ^5(2)+\left (-2812500 x^4-2250000 x^5 \log (2)-675000 x^6 \log ^2(2)-90000 x^7 \log ^3(2)-4500 x^8 \log ^4(2)\right ) \log (x)+\left (506250 x^3+303750 x^4 \log (2)+60750 x^5 \log ^2(2)+4050 x^6 \log ^3(2)\right ) \log ^2(x)+\left (-40500 x^2-16200 x^3 \log (2)-1620 x^4 \log ^2(2)\right ) \log ^3(x)+\left (1215 x+243 x^2 \log (2)\right ) \log ^4(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 {36 (5 x (5+x \log (2))-3 \log (x))^3 (-5-x \log (2)+(5+x \log (4)) \log (x))}{x (5+x \log (2)) \left (1867 x^4 (5+x \log (2))^4-4500 x^3 (5+x \log (2))^3 \log (x)+4050 x^2 (5+x \log (2))^2 \log ^2(x)-1620 x (5+x \log (2)) \log ^3(x)+243 \log ^4(x)\right )} \, dx\\ &=36 \int \frac {(5 x (5+x \log (2))-3 \log (x))^3 (-5-x \log (2)+(5+x \log (4)) \log (x))}{x (5+x \log (2)) \left (1867 x^4 (5+x \log (2))^4-4500 x^3 (5+x \log (2))^3 \log (x)+4050 x^2 (5+x \log (2))^2 \log ^2(x)-1620 x (5+x \log (2)) \log ^3(x)+243 \log ^4(x)\right )} \, dx\\ &=36 \int \left (\frac {-5-x \log (4)}{9 x (5+x \log (2))}+\frac {-140625 x^3+1166875 x^4 \left (1-\frac {135 \log (2)}{1867}\right )+1867 x^8 \log ^3(2) \log (4)+140025 x^6 \log ^2(2) \left (1-\frac {15 \log (2)}{1867}+\frac {\log (4)}{\log (2)}\right )+700125 x^5 \log (2) \left (1-\frac {45 \log (2)}{1867}+\frac {\log (4)}{\log (8)}\right )+9335 x^7 \log ^3(2) \left (1+\frac {\log (64)}{\log (2)}\right )+50625 x^2 \log (x)-421875 x^3 \left (1-\frac {6 \log (2)}{125}\right ) \log (x)-168750 x^4 \left (2-\frac {3 \log (2)}{250}\right ) \log (2) \log (x)-3375 x^6 \log ^2(2) \log (4) \log (x)-16875 x^5 \log ^2(2) \left (1+\frac {\log (16)}{\log (2)}\right ) \log (x)-6075 x \log ^2(x)+50625 x^2 \left (1-\frac {3 \log (2)}{125}\right ) \log ^2(x)+2025 x^4 \log (2) \log (4) \log ^2(x)+10125 x^3 \log (2) \left (1+\frac {\log (4)}{\log (2)}\right ) \log ^2(x)+243 \log ^3(x)-2025 x \log ^3(x)-405 x^2 \log (4) \log ^3(x)}{9 x \left (1166875 x^4+933500 x^5 \log (2)+280050 x^6 \log ^2(2)+37340 x^7 \log ^3(2)+1867 x^8 \log ^4(2)-562500 x^3 \log (x)-337500 x^4 \log (2) \log (x)-67500 x^5 \log ^2(2) \log (x)-4500 x^6 \log ^3(2) \log (x)+101250 x^2 \log ^2(x)+40500 x^3 \log (2) \log ^2(x)+4050 x^4 \log ^2(2) \log ^2(x)-8100 x \log ^3(x)-1620 x^2 \log (2) \log ^3(x)+243 \log ^4(x)\right )}\right ) \, dx\\ &=4 \int \frac {-5-x \log (4)}{x (5+x \log (2))} \, dx+4 \int \frac {-140625 x^3+1166875 x^4 \left (1-\frac {135 \log (2)}{1867}\right )+1867 x^8 \log ^3(2) \log (4)+140025 x^6 \log ^2(2) \left (1-\frac {15 \log (2)}{1867}+\frac {\log (4)}{\log (2)}\right )+700125 x^5 \log (2) \left (1-\frac {45 \log (2)}{1867}+\frac {\log (4)}{\log (8)}\right )+9335 x^7 \log ^3(2) \left (1+\frac {\log (64)}{\log (2)}\right )+50625 x^2 \log (x)-421875 x^3 \left (1-\frac {6 \log (2)}{125}\right ) \log (x)-168750 x^4 \left (2-\frac {3 \log (2)}{250}\right ) \log (2) \log (x)-3375 x^6 \log ^2(2) \log (4) \log (x)-16875 x^5 \log ^2(2) \left (1+\frac {\log (16)}{\log (2)}\right ) \log (x)-6075 x \log ^2(x)+50625 x^2 \left (1-\frac {3 \log (2)}{125}\right ) \log ^2(x)+2025 x^4 \log (2) \log (4) \log ^2(x)+10125 x^3 \log (2) \left (1+\frac {\log (4)}{\log (2)}\right ) \log ^2(x)+243 \log ^3(x)-2025 x \log ^3(x)-405 x^2 \log (4) \log ^3(x)}{x \left (1166875 x^4+933500 x^5 \log (2)+280050 x^6 \log ^2(2)+37340 x^7 \log ^3(2)+1867 x^8 \log ^4(2)-562500 x^3 \log (x)-337500 x^4 \log (2) \log (x)-67500 x^5 \log ^2(2) \log (x)-4500 x^6 \log ^3(2) \log (x)+101250 x^2 \log ^2(x)+40500 x^3 \log (2) \log ^2(x)+4050 x^4 \log ^2(2) \log ^2(x)-8100 x \log ^3(x)-1620 x^2 \log (2) \log ^3(x)+243 \log ^4(x)\right )} \, dx\\ &=4 \int \left (-\frac {1}{x}-\frac {\log (2)}{5+x \log (2)}\right ) \, dx+4 \int \frac {x^3 \left (-140625 \log (8)-625 x (-1867+135 \log (2)) \log (8)-75 x^3 \log (2) \left (-1867 \log (2)+15 \log ^2(2)-1867 \log (4)\right ) \log (8)+1867 x^5 \log ^3(2) \log (4) \log (8)-375 x^2 \log (2) (-1867 \log (4)+(-1867+45 \log (2)) \log (8))+9335 x^4 \log ^2(2) \log (8) \log (128)\right )-675 x^2 \log (8) \left (-75+x (625-30 \log (2))+5 x^4 \log ^2(2) \log (4)-x^2 \log (2) (-500+\log (8))+25 x^3 \log (2) \log (32)\right ) \log (x)+405 x (5+x \log (2)) \left (-3+25 x+5 x^2 \log (4)\right ) \log (8) \log ^2(x)-81 \left (-3+25 x+5 x^2 \log (4)\right ) \log (8) \log ^3(x)}{x \log (8) \left (1867 x^4 (5+x \log (2))^4-4500 x^3 (5+x \log (2))^3 \log (x)+4050 x^2 (5+x \log (2))^2 \log ^2(x)-1620 x (5+x \log (2)) \log ^3(x)+243 \log ^4(x)\right )} \, dx\\ &=-4 \log (x)-4 \log (5+x \log (2))+\frac {4 \int \frac {x^3 \left (-140625 \log (8)-625 x (-1867+135 \log (2)) \log (8)-75 x^3 \log (2) \left (-1867 \log (2)+15 \log ^2(2)-1867 \log (4)\right ) \log (8)+1867 x^5 \log ^3(2) \log (4) \log (8)-375 x^2 \log (2) (-1867 \log (4)+(-1867+45 \log (2)) \log (8))+9335 x^4 \log ^2(2) \log (8) \log (128)\right )-675 x^2 \log (8) \left (-75+x (625-30 \log (2))+5 x^4 \log ^2(2) \log (4)-x^2 \log (2) (-500+\log (8))+25 x^3 \log (2) \log (32)\right ) \log (x)+405 x (5+x \log (2)) \left (-3+25 x+5 x^2 \log (4)\right ) \log (8) \log ^2(x)-81 \left (-3+25 x+5 x^2 \log (4)\right ) \log (8) \log ^3(x)}{x \left (1867 x^4 (5+x \log (2))^4-4500 x^3 (5+x \log (2))^3 \log (x)+4050 x^2 (5+x \log (2))^2 \log ^2(x)-1620 x (5+x \log (2)) \log ^3(x)+243 \log ^4(x)\right )} \, dx}{\log (8)}\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [F]
time = 0.77, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {-2812500 x^3-2250000 x^4 \log (2)-675000 x^5 \log ^2(2)-90000 x^6 \log ^3(2)-4500 x^7 \log ^4(2)+\left (1012500 x^2+2812500 x^3+\left (607500 x^3+2812500 x^4\right ) \log (2)+\left (121500 x^4+1012500 x^5\right ) \log ^2(2)+\left (8100 x^5+157500 x^6\right ) \log ^3(2)+9000 x^7 \log ^4(2)\right ) \log (x)+\left (-121500 x-1012500 x^2+\left (-48600 x^2-810000 x^3\right ) \log (2)+\left (-4860 x^3-202500 x^4\right ) \log ^2(2)-16200 x^5 \log ^3(2)\right ) \log ^2(x)+\left (4860+121500 x+\left (972 x+72900 x^2\right ) \log (2)+9720 x^3 \log ^2(2)\right ) \log ^3(x)+(-4860-1944 x \log (2)) \log ^4(x)}{5834375 x^5+5834375 x^6 \log (2)+2333750 x^7 \log ^2(2)+466750 x^8 \log ^3(2)+46675 x^9 \log ^4(2)+1867 x^{10} \log ^5(2)+\left (-2812500 x^4-2250000 x^5 \log (2)-675000 x^6 \log ^2(2)-90000 x^7 \log ^3(2)-4500 x^8 \log ^4(2)\right ) \log (x)+\left (506250 x^3+303750 x^4 \log (2)+60750 x^5 \log ^2(2)+4050 x^6 \log ^3(2)\right ) \log ^2(x)+\left (-40500 x^2-16200 x^3 \log (2)-1620 x^4 \log ^2(2)\right ) \log ^3(x)+\left (1215 x+243 x^2 \log (2)\right ) \log ^4(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(152\) vs.
\(2(22)=44\).
time = 2.44, size = 153, normalized size = 6.38
method | result | size |
risch | \(-4 \ln \left (x^{2} \ln \left (2\right )+5 x \right )+\ln \left (\ln \left (x \right )^{4}+\left (-\frac {20 x^{2} \ln \left (2\right )}{3}-\frac {100 x}{3}\right ) \ln \left (x \right )^{3}+\left (\frac {50 x^{4} \ln \left (2\right )^{2}}{3}+\frac {500 x^{3} \ln \left (2\right )}{3}+\frac {1250 x^{2}}{3}\right ) \ln \left (x \right )^{2}+\left (-\frac {500 x^{6} \ln \left (2\right )^{3}}{27}-\frac {2500 x^{5} \ln \left (2\right )^{2}}{9}-\frac {12500 x^{4} \ln \left (2\right )}{9}-\frac {62500 x^{3}}{27}\right ) \ln \left (x \right )+\frac {1867 x^{8} \ln \left (2\right )^{4}}{243}+\frac {37340 x^{7} \ln \left (2\right )^{3}}{243}+\frac {93350 x^{6} \ln \left (2\right )^{2}}{81}+\frac {933500 x^{5} \ln \left (2\right )}{243}+\frac {1166875 x^{4}}{243}\right )\) | \(137\) |
default | \(-4 \ln \left (x \right )-4 \ln \left (x +\frac {5}{\ln \left (2\right )}\right )+\ln \left (x^{8}+\frac {20 x^{7}}{\ln \left (2\right )}-\frac {150 \left (30 \ln \left (2\right ) \ln \left (x \right )-1867\right ) x^{6}}{1867 \ln \left (2\right )^{2}}-\frac {500 \left (135 \ln \left (2\right ) \ln \left (x \right )-1867\right ) x^{5}}{1867 \ln \left (2\right )^{3}}+\frac {25 \left (162 \ln \left (2\right )^{2} \ln \left (x \right )^{2}-13500 \ln \left (2\right ) \ln \left (x \right )+46675\right ) x^{4}}{1867 \ln \left (2\right )^{4}}+\frac {4500 \ln \left (x \right ) \left (9 \ln \left (2\right ) \ln \left (x \right )-125\right ) x^{3}}{1867 \ln \left (2\right )^{4}}-\frac {810 \ln \left (x \right )^{2} \left (2 \ln \left (2\right ) \ln \left (x \right )-125\right ) x^{2}}{1867 \ln \left (2\right )^{4}}-\frac {8100 \ln \left (x \right )^{3} x}{1867 \ln \left (2\right )^{4}}+\frac {243 \ln \left (x \right )^{4}}{1867 \ln \left (2\right )^{4}}\right )\) | \(153\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 136 vs.
\(2 (22) = 44\).
time = 0.54, size = 136, normalized size = 5.67 \begin {gather*} \log \left (\frac {1867}{243} \, x^{8} \log \left (2\right )^{4} + \frac {37340}{243} \, x^{7} \log \left (2\right )^{3} + \frac {93350}{81} \, x^{6} \log \left (2\right )^{2} + \frac {933500}{243} \, x^{5} \log \left (2\right ) + \frac {1166875}{243} \, x^{4} - \frac {20}{3} \, {\left (x^{2} \log \left (2\right ) + 5 \, x\right )} \log \left (x\right )^{3} + \log \left (x\right )^{4} + \frac {50}{3} \, {\left (x^{4} \log \left (2\right )^{2} + 10 \, x^{3} \log \left (2\right ) + 25 \, x^{2}\right )} \log \left (x\right )^{2} - \frac {500}{27} \, {\left (x^{6} \log \left (2\right )^{3} + 15 \, x^{5} \log \left (2\right )^{2} + 75 \, x^{4} \log \left (2\right ) + 125 \, x^{3}\right )} \log \left (x\right )\right ) - 4 \, \log \left (x \log \left (2\right ) + 5\right ) - 4 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 138 vs.
\(2 (22) = 44\).
time = 0.40, size = 138, normalized size = 5.75 \begin {gather*} \log \left (1867 \, x^{8} \log \left (2\right )^{4} + 37340 \, x^{7} \log \left (2\right )^{3} + 280050 \, x^{6} \log \left (2\right )^{2} + 933500 \, x^{5} \log \left (2\right ) + 1166875 \, x^{4} - 1620 \, {\left (x^{2} \log \left (2\right ) + 5 \, x\right )} \log \left (x\right )^{3} + 243 \, \log \left (x\right )^{4} + 4050 \, {\left (x^{4} \log \left (2\right )^{2} + 10 \, x^{3} \log \left (2\right ) + 25 \, x^{2}\right )} \log \left (x\right )^{2} - 4500 \, {\left (x^{6} \log \left (2\right )^{3} + 15 \, x^{5} \log \left (2\right )^{2} + 75 \, x^{4} \log \left (2\right ) + 125 \, x^{3}\right )} \log \left (x\right )\right ) - 4 \, \log \left (x^{2} \log \left (2\right ) + 5 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 173 vs.
\(2 (20) = 40\).
time = 1.92, size = 173, normalized size = 7.21 \begin {gather*} - 4 \log {\left (x^{2} \log {\left (2 \right )} + 5 x \right )} + \log {\left (\frac {1867 x^{8} \log {\left (2 \right )}^{4}}{243} + \frac {37340 x^{7} \log {\left (2 \right )}^{3}}{243} + \frac {93350 x^{6} \log {\left (2 \right )}^{2}}{81} + \frac {933500 x^{5} \log {\left (2 \right )}}{243} + \frac {1166875 x^{4}}{243} + \left (- \frac {20 x^{2} \log {\left (2 \right )}}{3} - \frac {100 x}{3}\right ) \log {\left (x \right )}^{3} + \left (\frac {50 x^{4} \log {\left (2 \right )}^{2}}{3} + \frac {500 x^{3} \log {\left (2 \right )}}{3} + \frac {1250 x^{2}}{3}\right ) \log {\left (x \right )}^{2} + \left (- \frac {500 x^{6} \log {\left (2 \right )}^{3}}{27} - \frac {2500 x^{5} \log {\left (2 \right )}^{2}}{9} - \frac {12500 x^{4} \log {\left (2 \right )}}{9} - \frac {62500 x^{3}}{27}\right ) \log {\left (x \right )} + \log {\left (x \right )}^{4} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 150 vs.
\(2 (22) = 44\).
time = 1.19, size = 150, normalized size = 6.25 \begin {gather*} \log \left (1867 \, x^{8} \log \left (2\right )^{4} + 37340 \, x^{7} \log \left (2\right )^{3} - 4500 \, x^{6} \log \left (2\right )^{3} \log \left (x\right ) + 280050 \, x^{6} \log \left (2\right )^{2} - 67500 \, x^{5} \log \left (2\right )^{2} \log \left (x\right ) + 4050 \, x^{4} \log \left (2\right )^{2} \log \left (x\right )^{2} + 933500 \, x^{5} \log \left (2\right ) - 337500 \, x^{4} \log \left (2\right ) \log \left (x\right ) + 40500 \, x^{3} \log \left (2\right ) \log \left (x\right )^{2} - 1620 \, x^{2} \log \left (2\right ) \log \left (x\right )^{3} + 1166875 \, x^{4} - 562500 \, x^{3} \log \left (x\right ) + 101250 \, x^{2} \log \left (x\right )^{2} - 8100 \, x \log \left (x\right )^{3} + 243 \, \log \left (x\right )^{4}\right ) - 4 \, \log \left (x \log \left (2\right ) + 5\right ) - 4 \, \log \left (x\right ) \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 {675000\,x^5\,{\ln \left (2\right )}^2+90000\,x^6\,{\ln \left (2\right )}^3+4500\,x^7\,{\ln \left (2\right )}^4-{\ln \left (x\right )}^3\,\left (121500\,x+9720\,x^3\,{\ln \left (2\right )}^2+\ln \left (2\right )\,\left (72900\,x^2+972\,x\right )+4860\right )+{\ln \left (x\right )}^4\,\left (1944\,x\,\ln \left (2\right )+4860\right )-\ln \left (x\right )\,\left (9000\,x^7\,{\ln \left (2\right )}^4+\ln \left (2\right )\,\left (2812500\,x^4+607500\,x^3\right )+1012500\,x^2+2812500\,x^3+{\ln \left (2\right )}^3\,\left (157500\,x^6+8100\,x^5\right )+{\ln \left (2\right )}^2\,\left (1012500\,x^5+121500\,x^4\right )\right )+2250000\,x^4\,\ln \left (2\right )+{\ln \left (x\right )}^2\,\left (121500\,x+16200\,x^5\,{\ln \left (2\right )}^3+\ln \left (2\right )\,\left (810000\,x^3+48600\,x^2\right )+1012500\,x^2+{\ln \left (2\right )}^2\,\left (202500\,x^4+4860\,x^3\right )\right )+2812500\,x^3}{2333750\,x^7\,{\ln \left (2\right )}^2+466750\,x^8\,{\ln \left (2\right )}^3+46675\,x^9\,{\ln \left (2\right )}^4+1867\,x^{10}\,{\ln \left (2\right )}^5+{\ln \left (x\right )}^4\,\left (243\,\ln \left (2\right )\,x^2+1215\,x\right )-\ln \left (x\right )\,\left (4500\,{\ln \left (2\right )}^4\,x^8+90000\,{\ln \left (2\right )}^3\,x^7+675000\,{\ln \left (2\right )}^2\,x^6+2250000\,\ln \left (2\right )\,x^5+2812500\,x^4\right )+5834375\,x^6\,\ln \left (2\right )+5834375\,x^5-{\ln \left (x\right )}^3\,\left (1620\,{\ln \left (2\right )}^2\,x^4+16200\,\ln \left (2\right )\,x^3+40500\,x^2\right )+{\ln \left (x\right )}^2\,\left (4050\,{\ln \left (2\right )}^3\,x^6+60750\,{\ln \left (2\right )}^2\,x^5+303750\,\ln \left (2\right )\,x^4+506250\,x^3\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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