Integrand size = 216, antiderivative size = 24 \[ \int \frac {240 x^4+1713 x^5+3776 x^6+3328 x^7+1024 x^8+\left (-52 x^3+384 x^4+960 x^5+512 x^6\right ) \log (4)+\left (-140 x^2-144 x^3\right ) \log ^2(4)+\left (-44 x-32 x^2\right ) \log ^3(4)-4 \log ^4(4)+\left (188 x^4+1136 x^5+1728 x^6+768 x^7+\left (-92 x^3+96 x^4+192 x^5\right ) \log (4)+\left (-84 x^2-48 x^3\right ) \log ^2(4)-12 x \log ^3(4)\right ) \log (x)+\left (48 x^4+240 x^5+192 x^6-36 x^3 \log (4)-12 x^2 \log ^2(4)\right ) \log ^2(x)+\left (4 x^4+16 x^5-4 x^3 \log (4)\right ) \log ^3(x)}{x^5} \, dx=x+\left (-1+\left (\frac {4 x (1+x)+\log (4)}{x}+\log (x)\right )^2\right )^2 \]
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Leaf count is larger than twice the leaf count of optimal. \(288\) vs. \(2(24)=48\).
Time = 0.38 (sec) , antiderivative size = 288, normalized size of antiderivative = 12.00, number of steps used = 35, number of rules used = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {14, 2404, 2341, 2332, 2338, 2333, 2339, 30, 2342} \[ \int \frac {240 x^4+1713 x^5+3776 x^6+3328 x^7+1024 x^8+\left (-52 x^3+384 x^4+960 x^5+512 x^6\right ) \log (4)+\left (-140 x^2-144 x^3\right ) \log ^2(4)+\left (-44 x-32 x^2\right ) \log ^3(4)-4 \log ^4(4)+\left (188 x^4+1136 x^5+1728 x^6+768 x^7+\left (-92 x^3+96 x^4+192 x^5\right ) \log (4)+\left (-84 x^2-48 x^3\right ) \log ^2(4)-12 x \log ^3(4)\right ) \log (x)+\left (48 x^4+240 x^5+192 x^6-36 x^3 \log (4)-12 x^2 \log ^2(4)\right ) \log ^2(x)+\left (4 x^4+16 x^5-4 x^3 \log (4)\right ) \log ^3(x)}{x^5} \, dx=256 x^4+\frac {\log ^4(4)}{x^4}+1024 x^3+\frac {4 \log ^3(4) \log (x)}{x^3}+\frac {16 \log ^3(4)}{x^3}+256 x^3 \log (x)-384 x^2+96 x^2 \log ^2(x)+\frac {6 \log ^2(4) \log ^2(x)}{x^2}+\frac {48 \log ^2(4) \log (x)}{x^2}+\frac {2 \log ^2(4) (35+8 \log (4))}{x^2}+\frac {24 \log ^2(4)}{x^2}+768 x^2 \log (x)+32 x^2 (59+8 \log (4))+384 x+\log ^4(x)+16 x \log ^3(x)+16 \log ^3(x)+\frac {4 \log (4) \log ^3(x)}{x}+192 x \log ^2(x)+2 (47+24 \log (4)) \log ^2(x)+\frac {48 \log (4) \log ^2(x)}{x}+16 x (71+12 \log (4)) \log (x)-384 x \log (x)+3 x (571+320 \log (4))-16 x (71+12 \log (4))+48 (5+8 \log (4)) \log (x)+\frac {4 \log (4) (23+12 \log (4)) \log (x)}{x}+\frac {96 \log (4) \log (x)}{x}+\frac {4 \log (4) (13+36 \log (4))}{x}+\frac {4 \log (4) (23+12 \log (4))}{x}+\frac {96 \log (4)}{x} \]
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Rule 14
Rule 30
Rule 2332
Rule 2333
Rule 2338
Rule 2339
Rule 2341
Rule 2342
Rule 2404
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {3328 x^7+1024 x^8+3776 x^6 \left (1+\frac {8 \log (4)}{59}\right )+1713 x^5 \left (1+\frac {320 \log (4)}{571}\right )-140 x^2 \left (1+\frac {8 \log (4)}{35}\right ) \log ^2(4)-44 x \log ^3(4)-4 \log ^4(4)+240 x^4 \left (1+\frac {8 \log (4)}{5}\right )-52 x^3 \log (4) \left (1+\frac {36 \log (4)}{13}\right )}{x^5}+\frac {4 \left (x+4 x^2-\log (4)\right ) \left (96 x^3+48 x^4+24 x \log (4)+3 \log ^2(4)+x^2 (47+24 \log (4))\right ) \log (x)}{x^4}+\frac {12 \left (x+4 x^2-\log (4)\right ) \left (4 x+4 x^2+\log (4)\right ) \log ^2(x)}{x^3}+\frac {4 \left (x+4 x^2-\log (4)\right ) \log ^3(x)}{x^2}\right ) \, dx \\ & = 4 \int \frac {\left (x+4 x^2-\log (4)\right ) \left (96 x^3+48 x^4+24 x \log (4)+3 \log ^2(4)+x^2 (47+24 \log (4))\right ) \log (x)}{x^4} \, dx+4 \int \frac {\left (x+4 x^2-\log (4)\right ) \log ^3(x)}{x^2} \, dx+12 \int \frac {\left (x+4 x^2-\log (4)\right ) \left (4 x+4 x^2+\log (4)\right ) \log ^2(x)}{x^3} \, dx+\int \frac {3328 x^7+1024 x^8+3776 x^6 \left (1+\frac {8 \log (4)}{59}\right )+1713 x^5 \left (1+\frac {320 \log (4)}{571}\right )-140 x^2 \left (1+\frac {8 \log (4)}{35}\right ) \log ^2(4)-44 x \log ^3(4)-4 \log ^4(4)+240 x^4 \left (1+\frac {8 \log (4)}{5}\right )-52 x^3 \log (4) \left (1+\frac {36 \log (4)}{13}\right )}{x^5} \, dx \\ & = 4 \int \left (432 x \log (x)+192 x^2 \log (x)-\frac {21 \log ^2(4) \log (x)}{x^3}-\frac {3 \log ^3(4) \log (x)}{x^4}-\frac {\log (4) (23+12 \log (4)) \log (x)}{x^2}+4 (71+12 \log (4)) \log (x)+\frac {(47+24 \log (4)) \log (x)}{x}\right ) \, dx+4 \int \left (4 \log ^3(x)+\frac {\log ^3(x)}{x}-\frac {\log (4) \log ^3(x)}{x^2}\right ) \, dx+12 \int \left (20 \log ^2(x)+\frac {4 \log ^2(x)}{x}+16 x \log ^2(x)-\frac {3 \log (4) \log ^2(x)}{x^2}-\frac {\log ^2(4) \log ^2(x)}{x^3}\right ) \, dx+\int \left (3328 x^2+1024 x^3-\frac {44 \log ^3(4)}{x^4}-\frac {4 \log ^4(4)}{x^5}+\frac {48 (5+8 \log (4))}{x}-\frac {4 \log ^2(4) (35+8 \log (4))}{x^3}+64 x (59+8 \log (4))-\frac {4 \log (4) (13+36 \log (4))}{x^2}+3 (571+320 \log (4))\right ) \, dx \\ & = \frac {3328 x^3}{3}+256 x^4+\frac {44 \log ^3(4)}{3 x^3}+\frac {\log ^4(4)}{x^4}+\frac {2 \log ^2(4) (35+8 \log (4))}{x^2}+32 x^2 (59+8 \log (4))+\frac {4 \log (4) (13+36 \log (4))}{x}+3 x (571+320 \log (4))+48 (5+8 \log (4)) \log (x)+4 \int \frac {\log ^3(x)}{x} \, dx+16 \int \log ^3(x) \, dx+48 \int \frac {\log ^2(x)}{x} \, dx+192 \int x \log ^2(x) \, dx+240 \int \log ^2(x) \, dx+768 \int x^2 \log (x) \, dx+1728 \int x \log (x) \, dx-(4 \log (4)) \int \frac {\log ^3(x)}{x^2} \, dx-(36 \log (4)) \int \frac {\log ^2(x)}{x^2} \, dx-\left (12 \log ^2(4)\right ) \int \frac {\log ^2(x)}{x^3} \, dx-\left (84 \log ^2(4)\right ) \int \frac {\log (x)}{x^3} \, dx-\left (12 \log ^3(4)\right ) \int \frac {\log (x)}{x^4} \, dx-(4 \log (4) (23+12 \log (4))) \int \frac {\log (x)}{x^2} \, dx+(16 (71+12 \log (4))) \int \log (x) \, dx+(4 (47+24 \log (4))) \int \frac {\log (x)}{x} \, dx \\ & = -432 x^2+1024 x^3+256 x^4+\frac {21 \log ^2(4)}{x^2}+\frac {16 \log ^3(4)}{x^3}+\frac {\log ^4(4)}{x^4}+\frac {2 \log ^2(4) (35+8 \log (4))}{x^2}+32 x^2 (59+8 \log (4))+\frac {4 \log (4) (23+12 \log (4))}{x}-16 x (71+12 \log (4))+\frac {4 \log (4) (13+36 \log (4))}{x}+3 x (571+320 \log (4))+864 x^2 \log (x)+256 x^3 \log (x)+\frac {42 \log ^2(4) \log (x)}{x^2}+\frac {4 \log ^3(4) \log (x)}{x^3}+48 (5+8 \log (4)) \log (x)+\frac {4 \log (4) (23+12 \log (4)) \log (x)}{x}+16 x (71+12 \log (4)) \log (x)+240 x \log ^2(x)+96 x^2 \log ^2(x)+\frac {36 \log (4) \log ^2(x)}{x}+\frac {6 \log ^2(4) \log ^2(x)}{x^2}+2 (47+24 \log (4)) \log ^2(x)+16 x \log ^3(x)+\frac {4 \log (4) \log ^3(x)}{x}+4 \text {Subst}\left (\int x^3 \, dx,x,\log (x)\right )-48 \int \log ^2(x) \, dx+48 \text {Subst}\left (\int x^2 \, dx,x,\log (x)\right )-192 \int x \log (x) \, dx-480 \int \log (x) \, dx-(12 \log (4)) \int \frac {\log ^2(x)}{x^2} \, dx-(72 \log (4)) \int \frac {\log (x)}{x^2} \, dx-\left (12 \log ^2(4)\right ) \int \frac {\log (x)}{x^3} \, dx \\ & = 480 x-384 x^2+1024 x^3+256 x^4+\frac {72 \log (4)}{x}+\frac {24 \log ^2(4)}{x^2}+\frac {16 \log ^3(4)}{x^3}+\frac {\log ^4(4)}{x^4}+\frac {2 \log ^2(4) (35+8 \log (4))}{x^2}+32 x^2 (59+8 \log (4))+\frac {4 \log (4) (23+12 \log (4))}{x}-16 x (71+12 \log (4))+\frac {4 \log (4) (13+36 \log (4))}{x}+3 x (571+320 \log (4))-480 x \log (x)+768 x^2 \log (x)+256 x^3 \log (x)+\frac {72 \log (4) \log (x)}{x}+\frac {48 \log ^2(4) \log (x)}{x^2}+\frac {4 \log ^3(4) \log (x)}{x^3}+48 (5+8 \log (4)) \log (x)+\frac {4 \log (4) (23+12 \log (4)) \log (x)}{x}+16 x (71+12 \log (4)) \log (x)+192 x \log ^2(x)+96 x^2 \log ^2(x)+\frac {48 \log (4) \log ^2(x)}{x}+\frac {6 \log ^2(4) \log ^2(x)}{x^2}+2 (47+24 \log (4)) \log ^2(x)+16 \log ^3(x)+16 x \log ^3(x)+\frac {4 \log (4) \log ^3(x)}{x}+\log ^4(x)+96 \int \log (x) \, dx-(24 \log (4)) \int \frac {\log (x)}{x^2} \, dx \\ & = 384 x-384 x^2+1024 x^3+256 x^4+\frac {96 \log (4)}{x}+\frac {24 \log ^2(4)}{x^2}+\frac {16 \log ^3(4)}{x^3}+\frac {\log ^4(4)}{x^4}+\frac {2 \log ^2(4) (35+8 \log (4))}{x^2}+32 x^2 (59+8 \log (4))+\frac {4 \log (4) (23+12 \log (4))}{x}-16 x (71+12 \log (4))+\frac {4 \log (4) (13+36 \log (4))}{x}+3 x (571+320 \log (4))-384 x \log (x)+768 x^2 \log (x)+256 x^3 \log (x)+\frac {96 \log (4) \log (x)}{x}+\frac {48 \log ^2(4) \log (x)}{x^2}+\frac {4 \log ^3(4) \log (x)}{x^3}+48 (5+8 \log (4)) \log (x)+\frac {4 \log (4) (23+12 \log (4)) \log (x)}{x}+16 x (71+12 \log (4)) \log (x)+192 x \log ^2(x)+96 x^2 \log ^2(x)+\frac {48 \log (4) \log ^2(x)}{x}+\frac {6 \log ^2(4) \log ^2(x)}{x^2}+2 (47+24 \log (4)) \log ^2(x)+16 \log ^3(x)+16 x \log ^3(x)+\frac {4 \log (4) \log ^3(x)}{x}+\log ^4(x) \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(242\) vs. \(2(24)=48\).
Time = 0.10 (sec) , antiderivative size = 242, normalized size of antiderivative = 10.08 \[ \int \frac {240 x^4+1713 x^5+3776 x^6+3328 x^7+1024 x^8+\left (-52 x^3+384 x^4+960 x^5+512 x^6\right ) \log (4)+\left (-140 x^2-144 x^3\right ) \log ^2(4)+\left (-44 x-32 x^2\right ) \log ^3(4)-4 \log ^4(4)+\left (188 x^4+1136 x^5+1728 x^6+768 x^7+\left (-92 x^3+96 x^4+192 x^5\right ) \log (4)+\left (-84 x^2-48 x^3\right ) \log ^2(4)-12 x \log ^3(4)\right ) \log (x)+\left (48 x^4+240 x^5+192 x^6-36 x^3 \log (4)-12 x^2 \log ^2(4)\right ) \log ^2(x)+\left (4 x^4+16 x^5-4 x^3 \log (4)\right ) \log ^3(x)}{x^5} \, dx=961 x+1504 x^2+1024 x^3+256 x^4+\frac {240 \log (4)}{x}+768 x \log (4)+256 x^2 \log (4)+\frac {94 \log ^2(4)}{x^2}+\frac {192 \log ^2(4)}{x}+\frac {16 \log ^3(4)}{x^3}+\frac {16 \log ^3(4)}{x^2}+\frac {\log ^4(4)}{x^4}+240 \log (x)+752 x \log (x)+768 x^2 \log (x)+256 x^3 \log (x)+384 \log (4) \log (x)+\frac {188 \log (4) \log (x)}{x}+192 x \log (4) \log (x)+\frac {48 \log ^2(4) \log (x)}{x^2}+\frac {48 \log ^2(4) \log (x)}{x}+\frac {4 \log ^3(4) \log (x)}{x^3}+94 \log ^2(x)+192 x \log ^2(x)+96 x^2 \log ^2(x)+48 \log (4) \log ^2(x)+\frac {48 \log (4) \log ^2(x)}{x}+\frac {6 \log ^2(4) \log ^2(x)}{x^2}+16 \log ^3(x)+16 x \log ^3(x)+\frac {4 \log (4) \log ^3(x)}{x}+\log ^4(x) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(229\) vs. \(2(26)=52\).
Time = 0.13 (sec) , antiderivative size = 230, normalized size of antiderivative = 9.58
method | result | size |
risch | \(\ln \left (x \right )^{4}+\frac {8 \left (2 x^{2}+\ln \left (2\right )+2 x \right ) \ln \left (x \right )^{3}}{x}+\frac {2 \left (48 x^{4}+48 x^{2} \ln \left (2\right )+96 x^{3}+12 \ln \left (2\right )^{2}+48 x \ln \left (2\right )+47 x^{2}\right ) \ln \left (x \right )^{2}}{x^{2}}+\frac {8 \left (32 x^{6}+48 x^{4} \ln \left (2\right )+96 x^{5}+24 x^{2} \ln \left (2\right )^{2}+94 x^{4}+4 \ln \left (2\right )^{3}+24 x \ln \left (2\right )^{2}+47 x^{2} \ln \left (2\right )\right ) \ln \left (x \right )}{x^{3}}+\frac {256 x^{8}+512 x^{6} \ln \left (2\right )+1024 x^{7}+768 x^{4} \ln \left (2\right ) \ln \left (x \right )+1536 x^{5} \ln \left (2\right )+1504 x^{6}+128 x^{2} \ln \left (2\right )^{3}+768 x^{3} \ln \left (2\right )^{2}+240 x^{4} \ln \left (x \right )+961 x^{5}+16 \ln \left (2\right )^{4}+128 x \ln \left (2\right )^{3}+376 x^{2} \ln \left (2\right )^{2}+480 x^{3} \ln \left (2\right )}{x^{4}}\) | \(230\) |
parallelrisch | \(\frac {96 \ln \left (x \right )^{2} x^{4} \ln \left (2\right )+8 x^{3} \ln \left (2\right ) \ln \left (x \right )^{3}+24 x^{2} \ln \left (2\right )^{2} \ln \left (x \right )^{2}+768 x^{4} \ln \left (2\right ) \ln \left (x \right )+32 x \ln \left (2\right )^{3} \ln \left (x \right )+376 x^{3} \ln \left (2\right ) \ln \left (x \right )+128 x \ln \left (2\right )^{3}+16 x^{4} \ln \left (x \right )^{3}+128 x^{2} \ln \left (2\right )^{3}+96 x^{6} \ln \left (x \right )^{2}+768 x^{6} \ln \left (x \right )+256 x^{7} \ln \left (x \right )+16 x^{5} \ln \left (x \right )^{3}+768 x^{3} \ln \left (2\right )^{2}+752 x^{5} \ln \left (x \right )+94 x^{4} \ln \left (x \right )^{2}+1536 x^{5} \ln \left (2\right )+512 x^{6} \ln \left (2\right )+376 x^{2} \ln \left (2\right )^{2}+480 x^{3} \ln \left (2\right )+240 x^{4} \ln \left (x \right )+x^{4} \ln \left (x \right )^{4}+192 x^{5} \ln \left (x \right )^{2}+16 \ln \left (2\right )^{4}+1024 x^{7}+256 x^{8}+1504 x^{6}+961 x^{5}+192 \ln \left (2\right )^{2} \ln \left (x \right ) x^{3}+192 \ln \left (2\right )^{2} \ln \left (x \right ) x^{2}+384 \ln \left (2\right ) \ln \left (x \right ) x^{5}+96 x^{3} \ln \left (2\right ) \ln \left (x \right )^{2}}{x^{4}}\) | \(272\) |
parts | \(961 x +192 x \ln \left (x \right )^{2}+1920 x \ln \left (2\right )+512 x^{2} \ln \left (2\right )+96 \ln \left (2\right ) \ln \left (x \right )^{2}+752 x \ln \left (x \right )-72 \ln \left (2\right ) \left (-\frac {\ln \left (x \right )^{2}}{x}-\frac {2 \ln \left (x \right )}{x}-\frac {2}{x}\right )-96 \ln \left (2\right )^{3} \left (-\frac {\ln \left (x \right )}{3 x^{3}}-\frac {1}{9 x^{3}}\right )-184 \ln \left (2\right ) \left (-\frac {\ln \left (x \right )}{x}-\frac {1}{x}\right )-192 \ln \left (2\right )^{2} \left (-\frac {\ln \left (x \right )}{x}-\frac {1}{x}\right )-336 \ln \left (2\right )^{2} \left (-\frac {\ln \left (x \right )}{2 x^{2}}-\frac {1}{4 x^{2}}\right )-8 \ln \left (2\right ) \left (-\frac {\ln \left (x \right )^{3}}{x}-\frac {3 \ln \left (x \right )^{2}}{x}-\frac {6 \ln \left (x \right )}{x}-\frac {6}{x}\right )-48 \ln \left (2\right )^{2} \left (-\frac {\ln \left (x \right )^{2}}{2 x^{2}}-\frac {\ln \left (x \right )}{2 x^{2}}-\frac {1}{4 x^{2}}\right )+\frac {16 \ln \left (2\right )^{4}}{x^{4}}+384 \ln \left (2\right ) \left (x \ln \left (x \right )-x \right )+\frac {352 \ln \left (2\right )^{3}}{3 x^{3}}+16 x \ln \left (x \right )^{3}+96 x^{2} \ln \left (x \right )^{2}+\ln \left (x \right )^{4}+16 \ln \left (x \right )^{3}+94 \ln \left (x \right )^{2}+256 x^{4}+1024 x^{3}+1504 x^{2}+256 x^{3} \ln \left (x \right )+768 x^{2} \ln \left (x \right )-\left (-768 \ln \left (2\right )-240\right ) \ln \left (x \right )+\frac {8 \ln \left (2\right ) \left (72 \ln \left (2\right )+13\right )}{x}+\frac {8 \ln \left (2\right )^{2} \left (16 \ln \left (2\right )+35\right )}{x^{2}}\) | \(329\) |
default | \(961 x +\frac {576 \ln \left (2\right )^{2}}{x}+\frac {280 \ln \left (2\right )^{2}}{x^{2}}+768 \ln \left (2\right ) \ln \left (x \right )+\frac {104 \ln \left (2\right )}{x}+192 x \ln \left (x \right )^{2}+1920 x \ln \left (2\right )+512 x^{2} \ln \left (2\right )+96 \ln \left (2\right ) \ln \left (x \right )^{2}+752 x \ln \left (x \right )-72 \ln \left (2\right ) \left (-\frac {\ln \left (x \right )^{2}}{x}-\frac {2 \ln \left (x \right )}{x}-\frac {2}{x}\right )-96 \ln \left (2\right )^{3} \left (-\frac {\ln \left (x \right )}{3 x^{3}}-\frac {1}{9 x^{3}}\right )-184 \ln \left (2\right ) \left (-\frac {\ln \left (x \right )}{x}-\frac {1}{x}\right )-192 \ln \left (2\right )^{2} \left (-\frac {\ln \left (x \right )}{x}-\frac {1}{x}\right )-336 \ln \left (2\right )^{2} \left (-\frac {\ln \left (x \right )}{2 x^{2}}-\frac {1}{4 x^{2}}\right )-8 \ln \left (2\right ) \left (-\frac {\ln \left (x \right )^{3}}{x}-\frac {3 \ln \left (x \right )^{2}}{x}-\frac {6 \ln \left (x \right )}{x}-\frac {6}{x}\right )-48 \ln \left (2\right )^{2} \left (-\frac {\ln \left (x \right )^{2}}{2 x^{2}}-\frac {\ln \left (x \right )}{2 x^{2}}-\frac {1}{4 x^{2}}\right )+\frac {128 \ln \left (2\right )^{3}}{x^{2}}+\frac {16 \ln \left (2\right )^{4}}{x^{4}}+384 \ln \left (2\right ) \left (x \ln \left (x \right )-x \right )+\frac {352 \ln \left (2\right )^{3}}{3 x^{3}}+16 x \ln \left (x \right )^{3}+96 x^{2} \ln \left (x \right )^{2}+\ln \left (x \right )^{4}+16 \ln \left (x \right )^{3}+240 \ln \left (x \right )+94 \ln \left (x \right )^{2}+256 x^{4}+1024 x^{3}+1504 x^{2}+256 x^{3} \ln \left (x \right )+768 x^{2} \ln \left (x \right )\) | \(335\) |
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Leaf count of result is larger than twice the leaf count of optimal. 216 vs. \(2 (25) = 50\).
Time = 0.23 (sec) , antiderivative size = 216, normalized size of antiderivative = 9.00 \[ \int \frac {240 x^4+1713 x^5+3776 x^6+3328 x^7+1024 x^8+\left (-52 x^3+384 x^4+960 x^5+512 x^6\right ) \log (4)+\left (-140 x^2-144 x^3\right ) \log ^2(4)+\left (-44 x-32 x^2\right ) \log ^3(4)-4 \log ^4(4)+\left (188 x^4+1136 x^5+1728 x^6+768 x^7+\left (-92 x^3+96 x^4+192 x^5\right ) \log (4)+\left (-84 x^2-48 x^3\right ) \log ^2(4)-12 x \log ^3(4)\right ) \log (x)+\left (48 x^4+240 x^5+192 x^6-36 x^3 \log (4)-12 x^2 \log ^2(4)\right ) \log ^2(x)+\left (4 x^4+16 x^5-4 x^3 \log (4)\right ) \log ^3(x)}{x^5} \, dx=\frac {256 \, x^{8} + x^{4} \log \left (x\right )^{4} + 1024 \, x^{7} + 1504 \, x^{6} + 961 \, x^{5} + 128 \, {\left (x^{2} + x\right )} \log \left (2\right )^{3} + 16 \, \log \left (2\right )^{4} + 8 \, {\left (2 \, x^{5} + 2 \, x^{4} + x^{3} \log \left (2\right )\right )} \log \left (x\right )^{3} + 8 \, {\left (96 \, x^{3} + 47 \, x^{2}\right )} \log \left (2\right )^{2} + 2 \, {\left (48 \, x^{6} + 96 \, x^{5} + 47 \, x^{4} + 12 \, x^{2} \log \left (2\right )^{2} + 48 \, {\left (x^{4} + x^{3}\right )} \log \left (2\right )\right )} \log \left (x\right )^{2} + 32 \, {\left (16 \, x^{6} + 48 \, x^{5} + 15 \, x^{3}\right )} \log \left (2\right ) + 8 \, {\left (32 \, x^{7} + 96 \, x^{6} + 94 \, x^{5} + 30 \, x^{4} + 4 \, x \log \left (2\right )^{3} + 24 \, {\left (x^{3} + x^{2}\right )} \log \left (2\right )^{2} + {\left (48 \, x^{5} + 96 \, x^{4} + 47 \, x^{3}\right )} \log \left (2\right )\right )} \log \left (x\right )}{x^{4}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 226 vs. \(2 (22) = 44\).
Time = 0.72 (sec) , antiderivative size = 226, normalized size of antiderivative = 9.42 \[ \int \frac {240 x^4+1713 x^5+3776 x^6+3328 x^7+1024 x^8+\left (-52 x^3+384 x^4+960 x^5+512 x^6\right ) \log (4)+\left (-140 x^2-144 x^3\right ) \log ^2(4)+\left (-44 x-32 x^2\right ) \log ^3(4)-4 \log ^4(4)+\left (188 x^4+1136 x^5+1728 x^6+768 x^7+\left (-92 x^3+96 x^4+192 x^5\right ) \log (4)+\left (-84 x^2-48 x^3\right ) \log ^2(4)-12 x \log ^3(4)\right ) \log (x)+\left (48 x^4+240 x^5+192 x^6-36 x^3 \log (4)-12 x^2 \log ^2(4)\right ) \log ^2(x)+\left (4 x^4+16 x^5-4 x^3 \log (4)\right ) \log ^3(x)}{x^5} \, dx=256 x^{4} + 1024 x^{3} + x^{2} \cdot \left (512 \log {\left (2 \right )} + 1504\right ) + x \left (961 + 1536 \log {\left (2 \right )}\right ) + \log {\left (x \right )}^{4} + 48 \cdot \left (5 + 16 \log {\left (2 \right )}\right ) \log {\left (x \right )} + \frac {\left (16 x^{2} + 16 x + 8 \log {\left (2 \right )}\right ) \log {\left (x \right )}^{3}}{x} + \frac {\left (96 x^{4} + 192 x^{3} + 96 x^{2} \log {\left (2 \right )} + 94 x^{2} + 96 x \log {\left (2 \right )} + 24 \log {\left (2 \right )}^{2}\right ) \log {\left (x \right )}^{2}}{x^{2}} + \frac {\left (256 x^{6} + 768 x^{5} + 384 x^{4} \log {\left (2 \right )} + 752 x^{4} + 192 x^{2} \log {\left (2 \right )}^{2} + 376 x^{2} \log {\left (2 \right )} + 192 x \log {\left (2 \right )}^{2} + 32 \log {\left (2 \right )}^{3}\right ) \log {\left (x \right )}}{x^{3}} + \frac {x^{3} \cdot \left (480 \log {\left (2 \right )} + 768 \log {\left (2 \right )}^{2}\right ) + x^{2} \cdot \left (128 \log {\left (2 \right )}^{3} + 376 \log {\left (2 \right )}^{2}\right ) + 128 x \log {\left (2 \right )}^{3} + 16 \log {\left (2 \right )}^{4}}{x^{4}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 322 vs. \(2 (25) = 50\).
Time = 0.19 (sec) , antiderivative size = 322, normalized size of antiderivative = 13.42 \[ \int \frac {240 x^4+1713 x^5+3776 x^6+3328 x^7+1024 x^8+\left (-52 x^3+384 x^4+960 x^5+512 x^6\right ) \log (4)+\left (-140 x^2-144 x^3\right ) \log ^2(4)+\left (-44 x-32 x^2\right ) \log ^3(4)-4 \log ^4(4)+\left (188 x^4+1136 x^5+1728 x^6+768 x^7+\left (-92 x^3+96 x^4+192 x^5\right ) \log (4)+\left (-84 x^2-48 x^3\right ) \log ^2(4)-12 x \log ^3(4)\right ) \log (x)+\left (48 x^4+240 x^5+192 x^6-36 x^3 \log (4)-12 x^2 \log ^2(4)\right ) \log ^2(x)+\left (4 x^4+16 x^5-4 x^3 \log (4)\right ) \log ^3(x)}{x^5} \, dx=256 \, x^{4} + \frac {32}{3} \, {\left (\frac {3 \, \log \left (x\right )}{x^{3}} + \frac {1}{x^{3}}\right )} \log \left (2\right )^{3} + 256 \, x^{3} \log \left (x\right ) + \log \left (x\right )^{4} + 48 \, {\left (2 \, \log \left (x\right )^{2} - 2 \, \log \left (x\right ) + 1\right )} x^{2} + 1024 \, x^{3} + 512 \, x^{2} \log \left (2\right ) + 192 \, {\left (\frac {\log \left (x\right )}{x} + \frac {1}{x}\right )} \log \left (2\right )^{2} + 84 \, {\left (\frac {2 \, \log \left (x\right )}{x^{2}} + \frac {1}{x^{2}}\right )} \log \left (2\right )^{2} + 864 \, x^{2} \log \left (x\right ) + 96 \, \log \left (2\right ) \log \left (x\right )^{2} + 16 \, \log \left (x\right )^{3} + 16 \, {\left (\log \left (x\right )^{3} - 3 \, \log \left (x\right )^{2} + 6 \, \log \left (x\right ) - 6\right )} x + 240 \, {\left (\log \left (x\right )^{2} - 2 \, \log \left (x\right ) + 2\right )} x + 1456 \, x^{2} + 384 \, {\left (x \log \left (x\right ) - x\right )} \log \left (2\right ) + 1920 \, x \log \left (2\right ) + 184 \, {\left (\frac {\log \left (x\right )}{x} + \frac {1}{x}\right )} \log \left (2\right ) + 1136 \, x \log \left (x\right ) + 768 \, \log \left (2\right ) \log \left (x\right ) + 94 \, \log \left (x\right )^{2} + 577 \, x + \frac {8 \, {\left (\log \left (x\right )^{3} + 3 \, \log \left (x\right )^{2} + 6 \, \log \left (x\right ) + 6\right )} \log \left (2\right )}{x} + \frac {72 \, {\left (\log \left (x\right )^{2} + 2 \, \log \left (x\right ) + 2\right )} \log \left (2\right )}{x} + \frac {12 \, {\left (2 \, \log \left (x\right )^{2} + 2 \, \log \left (x\right ) + 1\right )} \log \left (2\right )^{2}}{x^{2}} + \frac {576 \, \log \left (2\right )^{2}}{x} + \frac {128 \, \log \left (2\right )^{3}}{x^{2}} + \frac {104 \, \log \left (2\right )}{x} + \frac {280 \, \log \left (2\right )^{2}}{x^{2}} + \frac {352 \, \log \left (2\right )^{3}}{3 \, x^{3}} + \frac {16 \, \log \left (2\right )^{4}}{x^{4}} + 240 \, \log \left (x\right ) \]
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\[ \int \frac {240 x^4+1713 x^5+3776 x^6+3328 x^7+1024 x^8+\left (-52 x^3+384 x^4+960 x^5+512 x^6\right ) \log (4)+\left (-140 x^2-144 x^3\right ) \log ^2(4)+\left (-44 x-32 x^2\right ) \log ^3(4)-4 \log ^4(4)+\left (188 x^4+1136 x^5+1728 x^6+768 x^7+\left (-92 x^3+96 x^4+192 x^5\right ) \log (4)+\left (-84 x^2-48 x^3\right ) \log ^2(4)-12 x \log ^3(4)\right ) \log (x)+\left (48 x^4+240 x^5+192 x^6-36 x^3 \log (4)-12 x^2 \log ^2(4)\right ) \log ^2(x)+\left (4 x^4+16 x^5-4 x^3 \log (4)\right ) \log ^3(x)}{x^5} \, dx=\int { \frac {1024 \, x^{8} + 3328 \, x^{7} + 3776 \, x^{6} + 1713 \, x^{5} + 240 \, x^{4} - 32 \, {\left (8 \, x^{2} + 11 \, x\right )} \log \left (2\right )^{3} - 64 \, \log \left (2\right )^{4} + 4 \, {\left (4 \, x^{5} + x^{4} - 2 \, x^{3} \log \left (2\right )\right )} \log \left (x\right )^{3} - 16 \, {\left (36 \, x^{3} + 35 \, x^{2}\right )} \log \left (2\right )^{2} + 24 \, {\left (8 \, x^{6} + 10 \, x^{5} + 2 \, x^{4} - 3 \, x^{3} \log \left (2\right ) - 2 \, x^{2} \log \left (2\right )^{2}\right )} \log \left (x\right )^{2} + 8 \, {\left (128 \, x^{6} + 240 \, x^{5} + 96 \, x^{4} - 13 \, x^{3}\right )} \log \left (2\right ) + 4 \, {\left (192 \, x^{7} + 432 \, x^{6} + 284 \, x^{5} + 47 \, x^{4} - 24 \, x \log \left (2\right )^{3} - 12 \, {\left (4 \, x^{3} + 7 \, x^{2}\right )} \log \left (2\right )^{2} + 2 \, {\left (48 \, x^{5} + 24 \, x^{4} - 23 \, x^{3}\right )} \log \left (2\right )\right )} \log \left (x\right )}{x^{5}} \,d x } \]
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Time = 13.82 (sec) , antiderivative size = 223, normalized size of antiderivative = 9.29 \[ \int \frac {240 x^4+1713 x^5+3776 x^6+3328 x^7+1024 x^8+\left (-52 x^3+384 x^4+960 x^5+512 x^6\right ) \log (4)+\left (-140 x^2-144 x^3\right ) \log ^2(4)+\left (-44 x-32 x^2\right ) \log ^3(4)-4 \log ^4(4)+\left (188 x^4+1136 x^5+1728 x^6+768 x^7+\left (-92 x^3+96 x^4+192 x^5\right ) \log (4)+\left (-84 x^2-48 x^3\right ) \log ^2(4)-12 x \log ^3(4)\right ) \log (x)+\left (48 x^4+240 x^5+192 x^6-36 x^3 \log (4)-12 x^2 \log ^2(4)\right ) \log ^2(x)+\left (4 x^4+16 x^5-4 x^3 \log (4)\right ) \log ^3(x)}{x^5} \, dx=x\,\left (1536\,\ln \left (2\right )+961\right )+\frac {128\,{\ln \left (2\right )}^3}{x^3}+\frac {16\,{\ln \left (2\right )}^4}{x^4}+192\,x\,{\ln \left (x\right )}^2+768\,x^2\,\ln \left (x\right )+16\,x\,{\ln \left (x\right )}^3+256\,x^3\,\ln \left (x\right )+16\,{\ln \left (x\right )}^3+{\ln \left (x\right )}^4+x^2\,\left (512\,\ln \left (2\right )+1504\right )+\ln \left (x\right )\,\left (768\,\ln \left (2\right )+240\right )+96\,x^2\,{\ln \left (x\right )}^2+{\ln \left (x\right )}^2\,\left (96\,\ln \left (2\right )+94\right )+1024\,x^3+256\,x^4+\frac {8\,{\ln \left (2\right )}^2\,\left (16\,\ln \left (2\right )+47\right )}{x^2}+\frac {24\,{\ln \left (2\right )}^2\,{\ln \left (x\right )}^2}{x^2}+\frac {96\,\ln \left (2\right )\,\left (8\,\ln \left (2\right )+5\right )}{x}+x\,\ln \left (x\right )\,\left (384\,\ln \left (2\right )+752\right )+\frac {96\,\ln \left (2\right )\,{\ln \left (x\right )}^2}{x}+\frac {192\,{\ln \left (2\right )}^2\,\ln \left (x\right )}{x^2}+\frac {32\,{\ln \left (2\right )}^3\,\ln \left (x\right )}{x^3}+\frac {\ln \left (256\right )\,{\ln \left (x\right )}^3}{x}+\frac {8\,\ln \left (2\right )\,\ln \left (x\right )\,\left (24\,\ln \left (2\right )+47\right )}{x} \]
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