Optimal. Leaf size=29 \[ 2 x+\left (-2-x-(5+x)^2+\log \left (\frac {x}{3}\right )-4 \log (\log (3))\right )^4 \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(599\) vs. \(2(29)=58\).
time = 0.47, antiderivative size = 599, normalized size of antiderivative = 20.66, number of steps
used = 35, number of rules used = 9, integrand size = 268, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.034, Rules used = {14, 2404,
2333, 2332, 2339, 30, 2342, 2341, 2338} \begin {gather*} x^8+44 x^7+\frac {2 x^6}{3}-4 x^6 \log \left (\frac {x}{3}\right )+\frac {4}{3} x^6 (625+12 \log (\log (3)))+\frac {132 x^5}{5}-132 x^5 \log \left (\frac {x}{3}\right )+\frac {44}{5} x^5 (1007+60 \log (\log (3)))+\frac {3 x^4}{4}+6 x^4 \log ^2\left (\frac {x}{3}\right )+x^4 \left (57775+96 \log ^2(\log (3))+7092 \log (\log (3))\right )-3 x^4 \log \left (\frac {x}{3}\right )-3 x^4 (591+16 \log (\log (3))) \log \left (\frac {x}{3}\right )+\frac {3}{4} x^4 (591+16 \log (\log (3)))+\frac {88 x^3}{3}+132 x^3 \log ^2\left (\frac {x}{3}\right )+\frac {44}{3} x^3 \left (16079+144 \log ^2(\log (3))+3372 \log (\log (3))\right )-88 x^3 \log \left (\frac {x}{3}\right )-44 x^3 (281+24 \log (\log (3))) \log \left (\frac {x}{3}\right )+\frac {44}{3} x^3 (281+24 \log (\log (3)))+3 x^2-4 x^2 \log ^3\left (\frac {x}{3}\right )+6 x^2 \log ^2\left (\frac {x}{3}\right )-6 x^2 \left (7817+32 \log ^2(\log (3))+1392 \log (\log (3))\right ) \log \left (\frac {x}{3}\right )+3 x^2 \left (7817+32 \log ^2(\log (3))+1392 \log (\log (3))\right )+12 x^2 (87+4 \log (\log (3))) \log ^2\left (\frac {x}{3}\right )+2 x^2 \left (292005+128 \log ^3(\log (3))+8352 \log ^2(\log (3))+93804 \log (\log (3))\right )-6 x^2 \log \left (\frac {x}{3}\right )-12 x^2 (87+4 \log (\log (3))) \log \left (\frac {x}{3}\right )+6 x^2 (87+4 \log (\log (3)))+264 x+\log ^4\left (\frac {x}{3}\right )-44 x \log ^3\left (\frac {x}{3}\right )-4 (27+4 \log (\log (3))) \log ^3\left (\frac {x}{3}\right )+132 x \log ^2\left (\frac {x}{3}\right )-132 x \left (675+16 \log ^2(\log (3))+208 \log (\log (3))\right ) \log \left (\frac {x}{3}\right )+132 x \left (675+16 \log ^2(\log (3))+208 \log (\log (3))\right )+264 x (13+2 \log (\log (3))) \log ^2\left (\frac {x}{3}\right )+6 (27+4 \log (\log (3)))^2 \log ^2\left (\frac {x}{3}\right )+2 x \left (384913+1408 \log ^3(\log (3))+27456 \log ^2(\log (3))+178200 \log (\log (3))\right )-264 x \log \left (\frac {x}{3}\right )-528 x (13+2 \log (\log (3))) \log \left (\frac {x}{3}\right )+528 x (13+2 \log (\log (3)))-4 (27+4 \log (\log (3)))^3 \log (x) \end {gather*}
Antiderivative was successfully verified.
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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 {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {4 \left (-1+11 x+2 x^2\right ) \log ^3\left (\frac {x}{3}\right )}{x}+\frac {12 \left (-1+11 x+2 x^2\right ) \log ^2\left (\frac {x}{3}\right ) \left (27+11 x+x^2+4 \log (\log (3))\right )}{x}-\frac {12 \left (-1+11 x+2 x^2\right ) \log \left (\frac {x}{3}\right ) \left (27+11 x+x^2+4 \log (\log (3))\right )^2}{x}+\frac {2 \left (154 x^7+4 x^8+2500 x^6 \left (1+\frac {12}{625} \log (\log (3))\right )+22154 x^5 \left (1+\frac {60 \log (\log (3))}{1007}\right )+115550 x^4 \left (1+\frac {12 \log (\log (3)) (591+8 \log (\log (3)))}{57775}\right )+353738 x^3 \left (1+\frac {12 \log (\log (3)) (281+12 \log (\log (3)))}{16079}\right )+384913 x \left (1+\frac {88 \log (\log (3)) \left (2025+312 \log (\log (3))+16 \log ^2(\log (3))\right )}{384913}\right )+584010 x^2 \left (1+\frac {4 \log (\log (3)) \left (23451+2088 \log (\log (3))+32 \log ^2(\log (3))\right )}{292005}\right )-39366 \left (1+\frac {4}{9} \log (\log (3)) \left (1+\frac {4 \log (\log (3)) (81+4 \log (\log (3)))}{2187}\right )\right )\right )}{x}\right ) \, dx\\ &=2 \int \frac {154 x^7+4 x^8+2500 x^6 \left (1+\frac {12}{625} \log (\log (3))\right )+22154 x^5 \left (1+\frac {60 \log (\log (3))}{1007}\right )+115550 x^4 \left (1+\frac {12 \log (\log (3)) (591+8 \log (\log (3)))}{57775}\right )+353738 x^3 \left (1+\frac {12 \log (\log (3)) (281+12 \log (\log (3)))}{16079}\right )+384913 x \left (1+\frac {88 \log (\log (3)) \left (2025+312 \log (\log (3))+16 \log ^2(\log (3))\right )}{384913}\right )+584010 x^2 \left (1+\frac {4 \log (\log (3)) \left (23451+2088 \log (\log (3))+32 \log ^2(\log (3))\right )}{292005}\right )-39366 \left (1+\frac {4}{9} \log (\log (3)) \left (1+\frac {4 \log (\log (3)) (81+4 \log (\log (3)))}{2187}\right )\right )}{x} \, dx-4 \int \frac {\left (-1+11 x+2 x^2\right ) \log ^3\left (\frac {x}{3}\right )}{x} \, dx+12 \int \frac {\left (-1+11 x+2 x^2\right ) \log ^2\left (\frac {x}{3}\right ) \left (27+11 x+x^2+4 \log (\log (3))\right )}{x} \, dx-12 \int \frac {\left (-1+11 x+2 x^2\right ) \log \left (\frac {x}{3}\right ) \left (27+11 x+x^2+4 \log (\log (3))\right )^2}{x} \, dx\\ &=2 \int \left (384913+154 x^6+4 x^7+178200 \log (\log (3))+27456 \log ^2(\log (3))+1408 \log ^3(\log (3))+4 x^5 (625+12 \log (\log (3)))+22 x^4 (1007+60 \log (\log (3)))+2 x^3 \left (57775+7092 \log (\log (3))+96 \log ^2(\log (3))\right )+22 x^2 \left (16079+3372 \log (\log (3))+144 \log ^2(\log (3))\right )-\frac {2 \left (19683+8748 \log (\log (3))+1296 \log ^2(\log (3))+64 \log ^3(\log (3))\right )}{x}+2 x \left (292005+93804 \log (\log (3))+8352 \log ^2(\log (3))+128 \log ^3(\log (3))\right )\right ) \, dx-4 \int \left (11 \log ^3\left (\frac {x}{3}\right )-\frac {\log ^3\left (\frac {x}{3}\right )}{x}+2 x \log ^3\left (\frac {x}{3}\right )\right ) \, dx+12 \int \left (33 x^2 \log ^2\left (\frac {x}{3}\right )+2 x^3 \log ^2\left (\frac {x}{3}\right )+\frac {\log ^2\left (\frac {x}{3}\right ) (-27-4 \log (\log (3)))}{x}+22 \log ^2\left (\frac {x}{3}\right ) (13+2 \log (\log (3)))+2 x \log ^2\left (\frac {x}{3}\right ) (87+4 \log (\log (3)))\right ) \, dx-12 \int \left (55 x^4 \log \left (\frac {x}{3}\right )+2 x^5 \log \left (\frac {x}{3}\right )+x^3 \log \left (\frac {x}{3}\right ) (591+16 \log (\log (3)))+11 x^2 \log \left (\frac {x}{3}\right ) (281+24 \log (\log (3)))+\frac {\log \left (\frac {x}{3}\right ) \left (-729-216 \log (\log (3))-16 \log ^2(\log (3))\right )}{x}+11 \log \left (\frac {x}{3}\right ) \left (675+208 \log (\log (3))+16 \log ^2(\log (3))\right )+x \log \left (\frac {x}{3}\right ) \left (7817+1392 \log (\log (3))+32 \log ^2(\log (3))\right )\right ) \, dx\\ &=44 x^7+x^8-4 \log (x) (27+4 \log (\log (3)))^3+\frac {4}{3} x^6 (625+12 \log (\log (3)))+\frac {44}{5} x^5 (1007+60 \log (\log (3)))+x^4 \left (57775+7092 \log (\log (3))+96 \log ^2(\log (3))\right )+\frac {44}{3} x^3 \left (16079+3372 \log (\log (3))+144 \log ^2(\log (3))\right )+2 x^2 \left (292005+93804 \log (\log (3))+8352 \log ^2(\log (3))+128 \log ^3(\log (3))\right )+2 x \left (384913+178200 \log (\log (3))+27456 \log ^2(\log (3))+1408 \log ^3(\log (3))\right )+4 \int \frac {\log ^3\left (\frac {x}{3}\right )}{x} \, dx-8 \int x \log ^3\left (\frac {x}{3}\right ) \, dx-24 \int x^5 \log \left (\frac {x}{3}\right ) \, dx+24 \int x^3 \log ^2\left (\frac {x}{3}\right ) \, dx-44 \int \log ^3\left (\frac {x}{3}\right ) \, dx+396 \int x^2 \log ^2\left (\frac {x}{3}\right ) \, dx-660 \int x^4 \log \left (\frac {x}{3}\right ) \, dx+(264 (13+2 \log (\log (3)))) \int \log ^2\left (\frac {x}{3}\right ) \, dx-(12 (27+4 \log (\log (3)))) \int \frac {\log ^2\left (\frac {x}{3}\right )}{x} \, dx+\left (12 (27+4 \log (\log (3)))^2\right ) \int \frac {\log \left (\frac {x}{3}\right )}{x} \, dx+(24 (87+4 \log (\log (3)))) \int x \log ^2\left (\frac {x}{3}\right ) \, dx-(12 (591+16 \log (\log (3)))) \int x^3 \log \left (\frac {x}{3}\right ) \, dx-(132 (281+24 \log (\log (3)))) \int x^2 \log \left (\frac {x}{3}\right ) \, dx-\left (132 \left (675+208 \log (\log (3))+16 \log ^2(\log (3))\right )\right ) \int \log \left (\frac {x}{3}\right ) \, dx-\left (12 \left (7817+1392 \log (\log (3))+32 \log ^2(\log (3))\right )\right ) \int x \log \left (\frac {x}{3}\right ) \, dx\\ &=\frac {132 x^5}{5}+\frac {2 x^6}{3}+44 x^7+x^8-132 x^5 \log \left (\frac {x}{3}\right )-4 x^6 \log \left (\frac {x}{3}\right )+132 x^3 \log ^2\left (\frac {x}{3}\right )+6 x^4 \log ^2\left (\frac {x}{3}\right )-44 x \log ^3\left (\frac {x}{3}\right )-4 x^2 \log ^3\left (\frac {x}{3}\right )+264 x \log ^2\left (\frac {x}{3}\right ) (13+2 \log (\log (3)))+6 \log ^2\left (\frac {x}{3}\right ) (27+4 \log (\log (3)))^2-4 \log (x) (27+4 \log (\log (3)))^3+12 x^2 \log ^2\left (\frac {x}{3}\right ) (87+4 \log (\log (3)))+\frac {4}{3} x^6 (625+12 \log (\log (3)))+\frac {3}{4} x^4 (591+16 \log (\log (3)))-3 x^4 \log \left (\frac {x}{3}\right ) (591+16 \log (\log (3)))+\frac {44}{3} x^3 (281+24 \log (\log (3)))-44 x^3 \log \left (\frac {x}{3}\right ) (281+24 \log (\log (3)))+\frac {44}{5} x^5 (1007+60 \log (\log (3)))+132 x \left (675+208 \log (\log (3))+16 \log ^2(\log (3))\right )-132 x \log \left (\frac {x}{3}\right ) \left (675+208 \log (\log (3))+16 \log ^2(\log (3))\right )+3 x^2 \left (7817+1392 \log (\log (3))+32 \log ^2(\log (3))\right )-6 x^2 \log \left (\frac {x}{3}\right ) \left (7817+1392 \log (\log (3))+32 \log ^2(\log (3))\right )+x^4 \left (57775+7092 \log (\log (3))+96 \log ^2(\log (3))\right )+\frac {44}{3} x^3 \left (16079+3372 \log (\log (3))+144 \log ^2(\log (3))\right )+2 x^2 \left (292005+93804 \log (\log (3))+8352 \log ^2(\log (3))+128 \log ^3(\log (3))\right )+2 x \left (384913+178200 \log (\log (3))+27456 \log ^2(\log (3))+1408 \log ^3(\log (3))\right )+4 \text {Subst}\left (\int x^3 \, dx,x,\log \left (\frac {x}{3}\right )\right )-12 \int x^3 \log \left (\frac {x}{3}\right ) \, dx+12 \int x \log ^2\left (\frac {x}{3}\right ) \, dx+132 \int \log ^2\left (\frac {x}{3}\right ) \, dx-264 \int x^2 \log \left (\frac {x}{3}\right ) \, dx-(528 (13+2 \log (\log (3)))) \int \log \left (\frac {x}{3}\right ) \, dx-(12 (27+4 \log (\log (3)))) \text {Subst}\left (\int x^2 \, dx,x,\log \left (\frac {x}{3}\right )\right )-(24 (87+4 \log (\log (3)))) \int x \log \left (\frac {x}{3}\right ) \, dx\\ &=\frac {88 x^3}{3}+\frac {3 x^4}{4}+\frac {132 x^5}{5}+\frac {2 x^6}{3}+44 x^7+x^8-88 x^3 \log \left (\frac {x}{3}\right )-3 x^4 \log \left (\frac {x}{3}\right )-132 x^5 \log \left (\frac {x}{3}\right )-4 x^6 \log \left (\frac {x}{3}\right )+132 x \log ^2\left (\frac {x}{3}\right )+6 x^2 \log ^2\left (\frac {x}{3}\right )+132 x^3 \log ^2\left (\frac {x}{3}\right )+6 x^4 \log ^2\left (\frac {x}{3}\right )-44 x \log ^3\left (\frac {x}{3}\right )-4 x^2 \log ^3\left (\frac {x}{3}\right )+\log ^4\left (\frac {x}{3}\right )+528 x (13+2 \log (\log (3)))-528 x \log \left (\frac {x}{3}\right ) (13+2 \log (\log (3)))+264 x \log ^2\left (\frac {x}{3}\right ) (13+2 \log (\log (3)))-4 \log ^3\left (\frac {x}{3}\right ) (27+4 \log (\log (3)))+6 \log ^2\left (\frac {x}{3}\right ) (27+4 \log (\log (3)))^2-4 \log (x) (27+4 \log (\log (3)))^3+6 x^2 (87+4 \log (\log (3)))-12 x^2 \log \left (\frac {x}{3}\right ) (87+4 \log (\log (3)))+12 x^2 \log ^2\left (\frac {x}{3}\right ) (87+4 \log (\log (3)))+\frac {4}{3} x^6 (625+12 \log (\log (3)))+\frac {3}{4} x^4 (591+16 \log (\log (3)))-3 x^4 \log \left (\frac {x}{3}\right ) (591+16 \log (\log (3)))+\frac {44}{3} x^3 (281+24 \log (\log (3)))-44 x^3 \log \left (\frac {x}{3}\right ) (281+24 \log (\log (3)))+\frac {44}{5} x^5 (1007+60 \log (\log (3)))+132 x \left (675+208 \log (\log (3))+16 \log ^2(\log (3))\right )-132 x \log \left (\frac {x}{3}\right ) \left (675+208 \log (\log (3))+16 \log ^2(\log (3))\right )+3 x^2 \left (7817+1392 \log (\log (3))+32 \log ^2(\log (3))\right )-6 x^2 \log \left (\frac {x}{3}\right ) \left (7817+1392 \log (\log (3))+32 \log ^2(\log (3))\right )+x^4 \left (57775+7092 \log (\log (3))+96 \log ^2(\log (3))\right )+\frac {44}{3} x^3 \left (16079+3372 \log (\log (3))+144 \log ^2(\log (3))\right )+2 x^2 \left (292005+93804 \log (\log (3))+8352 \log ^2(\log (3))+128 \log ^3(\log (3))\right )+2 x \left (384913+178200 \log (\log (3))+27456 \log ^2(\log (3))+1408 \log ^3(\log (3))\right )-12 \int x \log \left (\frac {x}{3}\right ) \, dx-264 \int \log \left (\frac {x}{3}\right ) \, dx\\ &=264 x+3 x^2+\frac {88 x^3}{3}+\frac {3 x^4}{4}+\frac {132 x^5}{5}+\frac {2 x^6}{3}+44 x^7+x^8-264 x \log \left (\frac {x}{3}\right )-6 x^2 \log \left (\frac {x}{3}\right )-88 x^3 \log \left (\frac {x}{3}\right )-3 x^4 \log \left (\frac {x}{3}\right )-132 x^5 \log \left (\frac {x}{3}\right )-4 x^6 \log \left (\frac {x}{3}\right )+132 x \log ^2\left (\frac {x}{3}\right )+6 x^2 \log ^2\left (\frac {x}{3}\right )+132 x^3 \log ^2\left (\frac {x}{3}\right )+6 x^4 \log ^2\left (\frac {x}{3}\right )-44 x \log ^3\left (\frac {x}{3}\right )-4 x^2 \log ^3\left (\frac {x}{3}\right )+\log ^4\left (\frac {x}{3}\right )+528 x (13+2 \log (\log (3)))-528 x \log \left (\frac {x}{3}\right ) (13+2 \log (\log (3)))+264 x \log ^2\left (\frac {x}{3}\right ) (13+2 \log (\log (3)))-4 \log ^3\left (\frac {x}{3}\right ) (27+4 \log (\log (3)))+6 \log ^2\left (\frac {x}{3}\right ) (27+4 \log (\log (3)))^2-4 \log (x) (27+4 \log (\log (3)))^3+6 x^2 (87+4 \log (\log (3)))-12 x^2 \log \left (\frac {x}{3}\right ) (87+4 \log (\log (3)))+12 x^2 \log ^2\left (\frac {x}{3}\right ) (87+4 \log (\log (3)))+\frac {4}{3} x^6 (625+12 \log (\log (3)))+\frac {3}{4} x^4 (591+16 \log (\log (3)))-3 x^4 \log \left (\frac {x}{3}\right ) (591+16 \log (\log (3)))+\frac {44}{3} x^3 (281+24 \log (\log (3)))-44 x^3 \log \left (\frac {x}{3}\right ) (281+24 \log (\log (3)))+\frac {44}{5} x^5 (1007+60 \log (\log (3)))+132 x \left (675+208 \log (\log (3))+16 \log ^2(\log (3))\right )-132 x \log \left (\frac {x}{3}\right ) \left (675+208 \log (\log (3))+16 \log ^2(\log (3))\right )+3 x^2 \left (7817+1392 \log (\log (3))+32 \log ^2(\log (3))\right )-6 x^2 \log \left (\frac {x}{3}\right ) \left (7817+1392 \log (\log (3))+32 \log ^2(\log (3))\right )+x^4 \left (57775+7092 \log (\log (3))+96 \log ^2(\log (3))\right )+\frac {44}{3} x^3 \left (16079+3372 \log (\log (3))+144 \log ^2(\log (3))\right )+2 x^2 \left (292005+93804 \log (\log (3))+8352 \log ^2(\log (3))+128 \log ^3(\log (3))\right )+2 x \left (384913+178200 \log (\log (3))+27456 \log ^2(\log (3))+1408 \log ^3(\log (3))\right )\\ \end {aligned} \end {gather*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(235\) vs. \(2(29)=58\).
time = 0.11, size = 235, normalized size = 8.10 \begin {gather*} \log ^4\left (\frac {x}{3}\right )-4 \log (x) (27+4 \log (\log (3)))^3-4 \log ^3\left (\frac {x}{3}\right ) \left (27+11 x+x^2+4 \log (\log (3))\right )+6 \log ^2\left (\frac {x}{3}\right ) \left (27+11 x+x^2+4 \log (\log (3))\right )^2-4 x (11+x) \log \left (\frac {x}{3}\right ) \left (22 x^3+x^4+33 x (27+4 \log (\log (3)))+3 (27+4 \log (\log (3)))^2+2 x^2 (101+6 \log (\log (3)))\right )+x \left (866054+44 x^6+x^7+384912 \log (\log (3))+57024 \log ^2(\log (3))+2816 \log ^3(\log (3))+88 x^4 (101+6 \log (\log (3)))+2 x^5 (417+8 \log (\log (3)))+2 x (27+4 \log (\log (3)))^2 (417+8 \log (\log (3)))+88 x^2 \left (2727+566 \log (\log (3))+24 \log ^2(\log (3))\right )+x^3 \left (58219+7104 \log (\log (3))+96 \log ^2(\log (3))\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(519\) vs.
\(2(27)=54\).
time = 0.15, size = 520, normalized size = 17.93 Too large to display
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. 569 vs.
\(2 (25) = 50\).
time = 0.28, size = 569, normalized size = 19.62 \begin {gather*} x^{8} + 44 \, x^{7} - 4 \, x^{6} \log \left (\frac {1}{3} \, x\right ) + 16 \, x^{6} \log \left (\log \left (3\right )\right ) + 834 \, x^{6} - 132 \, x^{5} \log \left (\frac {1}{3} \, x\right ) + 528 \, x^{5} \log \left (\log \left (3\right )\right ) + 96 \, x^{4} \log \left (\log \left (3\right )\right )^{2} + \frac {3}{4} \, {\left (8 \, \log \left (\frac {1}{3} \, x\right )^{2} - 4 \, \log \left (\frac {1}{3} \, x\right ) + 1\right )} x^{4} + 8888 \, x^{5} - 1773 \, x^{4} \log \left (\frac {1}{3} \, x\right ) + 7092 \, x^{4} \log \left (\log \left (3\right )\right ) + 2112 \, x^{3} \log \left (\log \left (3\right )\right )^{2} + 256 \, x^{2} \log \left (\log \left (3\right )\right )^{3} + \frac {44}{3} \, {\left (9 \, \log \left (\frac {1}{3} \, x\right )^{2} - 6 \, \log \left (\frac {1}{3} \, x\right ) + 2\right )} x^{3} + \frac {232873}{4} \, x^{4} - 12364 \, x^{3} \log \left (\frac {1}{3} \, x\right ) + \log \left (\frac {1}{3} \, x\right )^{4} + 24 \, {\left (2 \, \log \left (\frac {1}{3} \, x\right )^{2} - 2 \, \log \left (\frac {1}{3} \, x\right ) + 1\right )} x^{2} \log \left (\log \left (3\right )\right ) + 49456 \, x^{3} \log \left (\log \left (3\right )\right ) - 16 \, \log \left (\frac {1}{3} \, x\right )^{3} \log \left (\log \left (3\right )\right ) + 16704 \, x^{2} \log \left (\log \left (3\right )\right )^{2} + 96 \, \log \left (\frac {1}{3} \, x\right )^{2} \log \left (\log \left (3\right )\right )^{2} + 2816 \, x \log \left (\log \left (3\right )\right )^{3} - 256 \, \log \left (x\right ) \log \left (\log \left (3\right )\right )^{3} - {\left (4 \, \log \left (\frac {1}{3} \, x\right )^{3} - 6 \, \log \left (\frac {1}{3} \, x\right )^{2} + 6 \, \log \left (\frac {1}{3} \, x\right ) - 3\right )} x^{2} + 522 \, {\left (2 \, \log \left (\frac {1}{3} \, x\right )^{2} - 2 \, \log \left (\frac {1}{3} \, x\right ) + 1\right )} x^{2} + \frac {719840}{3} \, x^{3} - 46902 \, x^{2} \log \left (\frac {1}{3} \, x\right ) - 108 \, \log \left (\frac {1}{3} \, x\right )^{3} + 528 \, {\left (\log \left (\frac {1}{3} \, x\right )^{2} - 2 \, \log \left (\frac {1}{3} \, x\right ) + 2\right )} x \log \left (\log \left (3\right )\right ) + 187608 \, x^{2} \log \left (\log \left (3\right )\right ) + 1296 \, \log \left (\frac {1}{3} \, x\right )^{2} \log \left (\log \left (3\right )\right ) - 96 \, {\left (2 \, x^{2} \log \left (\frac {1}{3} \, x\right ) - x^{2}\right )} \log \left (\log \left (3\right )\right )^{2} - 2112 \, {\left (x \log \left (\frac {1}{3} \, x\right ) - x\right )} \log \left (\log \left (3\right )\right )^{2} + 54912 \, x \log \left (\log \left (3\right )\right )^{2} - 5184 \, \log \left (x\right ) \log \left (\log \left (3\right )\right )^{2} - 44 \, {\left (\log \left (\frac {1}{3} \, x\right )^{3} - 3 \, \log \left (\frac {1}{3} \, x\right )^{2} + 6 \, \log \left (\frac {1}{3} \, x\right ) - 6\right )} x + 3432 \, {\left (\log \left (\frac {1}{3} \, x\right )^{2} - 2 \, \log \left (\frac {1}{3} \, x\right ) + 2\right )} x + 607461 \, x^{2} - 89100 \, x \log \left (\frac {1}{3} \, x\right ) + 4374 \, \log \left (\frac {1}{3} \, x\right )^{2} - 12 \, {\left (4 \, x^{4} \log \left (\frac {1}{3} \, x\right ) - x^{4}\right )} \log \left (\log \left (3\right )\right ) - 352 \, {\left (3 \, x^{3} \log \left (\frac {1}{3} \, x\right ) - x^{3}\right )} \log \left (\log \left (3\right )\right ) - 4176 \, {\left (2 \, x^{2} \log \left (\frac {1}{3} \, x\right ) - x^{2}\right )} \log \left (\log \left (3\right )\right ) - 27456 \, {\left (x \log \left (\frac {1}{3} \, x\right ) - x\right )} \log \left (\log \left (3\right )\right ) + 356400 \, x \log \left (\log \left (3\right )\right ) - 34992 \, \log \left (x\right ) \log \left (\log \left (3\right )\right ) + 858926 \, x - 78732 \, \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. 263 vs.
\(2 (25) = 50\).
time = 0.35, size = 263, normalized size = 9.07 \begin {gather*} x^{8} + 44 \, x^{7} + 834 \, x^{6} + 8888 \, x^{5} + 58219 \, x^{4} - 4 \, {\left (x^{2} + 11 \, x + 27\right )} \log \left (\frac {1}{3} \, x\right )^{3} + \log \left (\frac {1}{3} \, x\right )^{4} + 256 \, {\left (x^{2} + 11 \, x - \log \left (\frac {1}{3} \, x\right )\right )} \log \left (\log \left (3\right )\right )^{3} + 239976 \, x^{3} + 6 \, {\left (x^{4} + 22 \, x^{3} + 175 \, x^{2} + 594 \, x + 729\right )} \log \left (\frac {1}{3} \, x\right )^{2} + 96 \, {\left (x^{4} + 22 \, x^{3} + 175 \, x^{2} - 2 \, {\left (x^{2} + 11 \, x + 27\right )} \log \left (\frac {1}{3} \, x\right ) + \log \left (\frac {1}{3} \, x\right )^{2} + 594 \, x\right )} \log \left (\log \left (3\right )\right )^{2} + 607986 \, x^{2} - 4 \, {\left (x^{6} + 33 \, x^{5} + 444 \, x^{4} + 3113 \, x^{3} + 11988 \, x^{2} + 24057 \, x + 19683\right )} \log \left (\frac {1}{3} \, x\right ) + 16 \, {\left (x^{6} + 33 \, x^{5} + 444 \, x^{4} + 3113 \, x^{3} + 3 \, {\left (x^{2} + 11 \, x + 27\right )} \log \left (\frac {1}{3} \, x\right )^{2} - \log \left (\frac {1}{3} \, x\right )^{3} + 11988 \, x^{2} - 3 \, {\left (x^{4} + 22 \, x^{3} + 175 \, x^{2} + 594 \, x + 729\right )} \log \left (\frac {1}{3} \, x\right ) + 24057 \, x\right )} \log \left (\log \left (3\right )\right ) + 866054 \, x \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. 333 vs.
\(2 (24) = 48\).
time = 0.48, size = 333, normalized size = 11.48 \begin {gather*} x^{8} + 44 x^{7} + x^{6} \cdot \left (16 \log {\left (\log {\left (3 \right )} \right )} + 834\right ) + x^{5} \cdot \left (528 \log {\left (\log {\left (3 \right )} \right )} + 8888\right ) + x^{4} \cdot \left (96 \log {\left (\log {\left (3 \right )} \right )}^{2} + 7104 \log {\left (\log {\left (3 \right )} \right )} + 58219\right ) + x^{3} \cdot \left (2112 \log {\left (\log {\left (3 \right )} \right )}^{2} + 49808 \log {\left (\log {\left (3 \right )} \right )} + 239976\right ) + x^{2} \cdot \left (256 \log {\left (\log {\left (3 \right )} \right )}^{3} + 16800 \log {\left (\log {\left (3 \right )} \right )}^{2} + 191808 \log {\left (\log {\left (3 \right )} \right )} + 607986\right ) + x \left (2816 \log {\left (\log {\left (3 \right )} \right )}^{3} + 57024 \log {\left (\log {\left (3 \right )} \right )}^{2} + 384912 \log {\left (\log {\left (3 \right )} \right )} + 866054\right ) + \left (- 4 x^{2} - 44 x - 108 - 16 \log {\left (\log {\left (3 \right )} \right )}\right ) \log {\left (\frac {x}{3} \right )}^{3} + \left (6 x^{4} + 132 x^{3} + 48 x^{2} \log {\left (\log {\left (3 \right )} \right )} + 1050 x^{2} + 528 x \log {\left (\log {\left (3 \right )} \right )} + 3564 x + 96 \log {\left (\log {\left (3 \right )} \right )}^{2} + 1296 \log {\left (\log {\left (3 \right )} \right )} + 4374\right ) \log {\left (\frac {x}{3} \right )}^{2} + \left (- 4 x^{6} - 132 x^{5} - 1776 x^{4} - 48 x^{4} \log {\left (\log {\left (3 \right )} \right )} - 12452 x^{3} - 1056 x^{3} \log {\left (\log {\left (3 \right )} \right )} - 47952 x^{2} - 8400 x^{2} \log {\left (\log {\left (3 \right )} \right )} - 192 x^{2} \log {\left (\log {\left (3 \right )} \right )}^{2} - 96228 x - 28512 x \log {\left (\log {\left (3 \right )} \right )} - 2112 x \log {\left (\log {\left (3 \right )} \right )}^{2}\right ) \log {\left (\frac {x}{3} \right )} + \log {\left (\frac {x}{3} \right )}^{4} - 4 \left (4 \log {\left (\log {\left (3 \right )} \right )} + 27\right )^{3} \log {\left (x \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. 298 vs.
\(2 (25) = 50\).
time = 0.40, size = 298, normalized size = 10.28 \begin {gather*} x^{8} + 44 \, x^{7} + 2 \, x^{6} {\left (8 \, \log \left (\log \left (3\right )\right ) + 417\right )} + 88 \, x^{5} {\left (6 \, \log \left (\log \left (3\right )\right ) + 101\right )} + {\left (96 \, \log \left (\log \left (3\right )\right )^{2} + 7104 \, \log \left (\log \left (3\right )\right ) + 58219\right )} x^{4} + 88 \, {\left (24 \, \log \left (\log \left (3\right )\right )^{2} + 566 \, \log \left (\log \left (3\right )\right ) + 2727\right )} x^{3} - 4 \, {\left (x^{2} + 11 \, x + 4 \, \log \left (\log \left (3\right )\right ) + 27\right )} \log \left (\frac {1}{3} \, x\right )^{3} + \log \left (\frac {1}{3} \, x\right )^{4} + 2 \, {\left (128 \, \log \left (\log \left (3\right )\right )^{3} + 8400 \, \log \left (\log \left (3\right )\right )^{2} + 95904 \, \log \left (\log \left (3\right )\right ) + 303993\right )} x^{2} + 6 \, {\left (x^{4} + 22 \, x^{3} + x^{2} {\left (8 \, \log \left (\log \left (3\right )\right ) + 175\right )} + 22 \, x {\left (4 \, \log \left (\log \left (3\right )\right ) + 27\right )} + 16 \, \log \left (\log \left (3\right )\right )^{2} + 216 \, \log \left (\log \left (3\right )\right ) + 729\right )} \log \left (\frac {1}{3} \, x\right )^{2} + 2 \, {\left (1408 \, \log \left (\log \left (3\right )\right )^{3} + 28512 \, \log \left (\log \left (3\right )\right )^{2} + 192456 \, \log \left (\log \left (3\right )\right ) + 433027\right )} x - 4 \, {\left (x^{6} + 33 \, x^{5} + 12 \, x^{4} {\left (\log \left (\log \left (3\right )\right ) + 37\right )} + 11 \, x^{3} {\left (24 \, \log \left (\log \left (3\right )\right ) + 283\right )} + 12 \, {\left (4 \, \log \left (\log \left (3\right )\right )^{2} + 175 \, \log \left (\log \left (3\right )\right ) + 999\right )} x^{2} + 33 \, {\left (16 \, \log \left (\log \left (3\right )\right )^{2} + 216 \, \log \left (\log \left (3\right )\right ) + 729\right )} x\right )} \log \left (\frac {1}{3} \, x\right ) - 4 \, {\left (64 \, \log \left (\log \left (3\right )\right )^{3} + 1296 \, \log \left (\log \left (3\right )\right )^{2} + 8748 \, \log \left (\log \left (3\right )\right ) + 19683\right )} \log \left (\frac {1}{3} \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.02, size = 335, normalized size = 11.55 \begin {gather*} x^4\,\left (7104\,\ln \left (\ln \left (3\right )\right )+96\,{\ln \left (\ln \left (3\right )\right )}^2+58219\right )-\ln \left (x\right )\,\left (34992\,\ln \left (\ln \left (3\right )\right )+5184\,{\ln \left (\ln \left (3\right )\right )}^2+256\,{\ln \left (\ln \left (3\right )\right )}^3+78732\right )+x^3\,\left (49808\,\ln \left (\ln \left (3\right )\right )+2112\,{\ln \left (\ln \left (3\right )\right )}^2+239976\right )-44\,x\,{\ln \left (\frac {x}{3}\right )}^3-132\,x^5\,\ln \left (\frac {x}{3}\right )-4\,x^6\,\ln \left (\frac {x}{3}\right )-{\ln \left (\frac {x}{3}\right )}^3\,\left (16\,\ln \left (\ln \left (3\right )\right )+108\right )+x\,\left (384912\,\ln \left (\ln \left (3\right )\right )+57024\,{\ln \left (\ln \left (3\right )\right )}^2+2816\,{\ln \left (\ln \left (3\right )\right )}^3+866054\right )+{\ln \left (\frac {x}{3}\right )}^4+x^6\,\left (16\,\ln \left (\ln \left (3\right )\right )+834\right )+x^5\,\left (528\,\ln \left (\ln \left (3\right )\right )+8888\right )+44\,x^7+x^8-4\,x^2\,{\ln \left (\frac {x}{3}\right )}^3+132\,x^3\,{\ln \left (\frac {x}{3}\right )}^2+6\,x^4\,{\ln \left (\frac {x}{3}\right )}^2+6\,{\ln \left (\frac {x}{3}\right )}^2\,{\left (4\,\ln \left (\ln \left (3\right )\right )+27\right )}^2-132\,x\,\ln \left (\frac {x}{3}\right )\,{\left (4\,\ln \left (\ln \left (3\right )\right )+27\right )}^2-x^4\,\ln \left (\frac {x}{3}\right )\,\left (48\,\ln \left (\ln \left (3\right )\right )+1776\right )+x\,{\ln \left (\frac {x}{3}\right )}^2\,\left (528\,\ln \left (\ln \left (3\right )\right )+3564\right )-x^3\,\ln \left (\frac {x}{3}\right )\,\left (1056\,\ln \left (\ln \left (3\right )\right )+12452\right )+x^2\,{\ln \left (\frac {x}{3}\right )}^2\,\left (48\,\ln \left (\ln \left (3\right )\right )+1050\right )+2\,x^2\,{\left (4\,\ln \left (\ln \left (3\right )\right )+27\right )}^2\,\left (8\,\ln \left (\ln \left (3\right )\right )+417\right )-48\,x^2\,\ln \left (\frac {x}{3}\right )\,\left (\ln \left (\ln \left (3\right )\right )+37\right )\,\left (4\,\ln \left (\ln \left (3\right )\right )+27\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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