3.88.0 ∫ −2x−4x2−2x3+(4x+4x2) log(3)−2x log2(3)+(−8x−4x2+4x3+(6x−6x2) log(3)+2x log2(3)) log(x)+(20x+30x2−20x log(3)) log2(x)+50x log3(x) log3 (x) dx [8736]

Integrand size = 100, antiderivative size = 21 \[ \int \frac {-2 x-4 x^2-2 x^3+\left (4 x+4 x^2\right ) \log (3)-2 x \log ^2(3)+\left (-8 x-4 x^2+4 x^3+\left (6 x-6 x^2\right ) \log (3)+2 x \log ^2(3)\right ) \log (x)+\left (20 x+30 x^2-20 x \log (3)\right ) \log ^2(x)+50 x \log ^3(x)}{\log ^3(x)} \, dx=x^2 \left (-5-\frac {1+x-\log (3)}{\log (x)}\right )^2 \]

Rubi [C] (veriﬁed)

Result contains higher order function than in optimal. Order 4 vs. order 3 in optimal.

Time = 0.49 (sec) , antiderivative size = 193, normalized size of antiderivative = 9.19, number of steps used = 38, number of rules used = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {6, 6820, 12, 6874, 27, 2395, 2343, 2346, 2209, 2403} \[ \int \frac {-2 x-4 x^2-2 x^3+\left (4 x+4 x^2\right ) \log (3)-2 x \log ^2(3)+\left (-8 x-4 x^2+4 x^3+\left (6 x-6 x^2\right ) \log (3)+2 x \log ^2(3)\right ) \log (x)+\left (20 x+30 x^2-20 x \log (3)\right ) \log ^2(x)+50 x \log ^3(x)}{\log ^3(x)} \, dx=-4 \left (4-\log ^2(3)-\log (27)\right ) \operatorname {ExpIntegralEi}(2 \log (x))+30 \operatorname {ExpIntegralEi}(3 \log (x))-6 (2+\log (27)) \operatorname {ExpIntegralEi}(3 \log (x))-(2-\log (9))^2 \operatorname {ExpIntegralEi}(2 \log (x))+10 (2-\log (9)) \operatorname {ExpIntegralEi}(2 \log (x))-9 (2-\log (9)) \operatorname {ExpIntegralEi}(3 \log (x))+\frac {x^4}{\log ^2(x)}+\frac {x^3 (2-\log (9))}{\log ^2(x)}+\frac {2 x^3 (2+\log (27))}{\log (x)}+\frac {3 x^3 (2-\log (9))}{\log (x)}+25 x^2+\frac {2 x^2 \left (4-\log ^2(3)-\log (27)\right )}{\log (x)}+\frac {x^2 (2-\log (9))^2}{4 \log ^2(x)}+\frac {x^2 (2-\log (9))^2}{2 \log (x)} \]

Rubi steps \begin{align*} \text {integral}& = \int \frac {-4 x^2-2 x^3+\left (4 x+4 x^2\right ) \log (3)+x \left (-2-2 \log ^2(3)\right )+\left (-8 x-4 x^2+4 x^3+\left (6 x-6 x^2\right ) \log (3)+2 x \log ^2(3)\right ) \log (x)+\left (20 x+30 x^2-20 x \log (3)\right ) \log ^2(x)+50 x \log ^3(x)}{\log ^3(x)} \, dx \\ & = \int \frac {2 x \left (-1-x^2-\log ^2(3)+x (-2+\log (9))+\log (9)+\left (-4+2 x^2+\log ^2(3)+\log (27)-x (2+\log (27))\right ) \log (x)+5 (2+3 x-\log (9)) \log ^2(x)+25 \log ^3(x)\right )}{\log ^3(x)} \, dx \\ & = 2 \int \frac {x \left (-1-x^2-\log ^2(3)+x (-2+\log (9))+\log (9)+\left (-4+2 x^2+\log ^2(3)+\log (27)-x (2+\log (27))\right ) \log (x)+5 (2+3 x-\log (9)) \log ^2(x)+25 \log ^3(x)\right )}{\log ^3(x)} \, dx \\ & = 2 \int \left (25 x+\frac {x \left (-1-x^2-\log ^2(3)-x (2-\log (9))+\log (9)\right )}{\log ^3(x)}+\frac {x \left (-4+2 x^2+\log ^2(3)+\log (27)-x (2+\log (27))\right )}{\log ^2(x)}+\frac {5 x (2+3 x-\log (9))}{\log (x)}\right ) \, dx \\ & = 25 x^2+2 \int \frac {x \left (-1-x^2-\log ^2(3)-x (2-\log (9))+\log (9)\right )}{\log ^3(x)} \, dx+2 \int \frac {x \left (-4+2 x^2+\log ^2(3)+\log (27)-x (2+\log (27))\right )}{\log ^2(x)} \, dx+10 \int \frac {x (2+3 x-\log (9))}{\log (x)} \, dx \\ & = 25 x^2+2 \int \left (\frac {2 x^3}{\log ^2(x)}+\frac {x^2 (-2-\log (27))}{\log ^2(x)}+\frac {x \left (-4+\log ^2(3)+\log (27)\right )}{\log ^2(x)}\right ) \, dx+2 \int -\frac {x (2+2 x-\log (9))^2}{4 \log ^3(x)} \, dx+10 \int \left (\frac {3 x^2}{\log (x)}-\frac {x (-2+\log (9))}{\log (x)}\right ) \, dx \\ & = 25 x^2-\frac {1}{2} \int \frac {x (2+2 x-\log (9))^2}{\log ^3(x)} \, dx+4 \int \frac {x^3}{\log ^2(x)} \, dx+30 \int \frac {x^2}{\log (x)} \, dx+(10 (2-\log (9))) \int \frac {x}{\log (x)} \, dx-\left (2 \left (4-\log ^2(3)-\log (27)\right )\right ) \int \frac {x}{\log ^2(x)} \, dx-(2 (2+\log (27))) \int \frac {x^2}{\log ^2(x)} \, dx \\ & = 25 x^2-\frac {4 x^4}{\log (x)}+\frac {2 x^2 \left (4-\log ^2(3)-\log (27)\right )}{\log (x)}+\frac {2 x^3 (2+\log (27))}{\log (x)}-\frac {1}{2} \int \left (\frac {4 x^3}{\log ^3(x)}-\frac {4 x^2 (-2+\log (9))}{\log ^3(x)}+\frac {x (-2+\log (9))^2}{\log ^3(x)}\right ) \, dx+16 \int \frac {x^3}{\log (x)} \, dx+30 \text {Subst}\left (\int \frac {e^{3 x}}{x} \, dx,x,\log (x)\right )+(10 (2-\log (9))) \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right )-\left (4 \left (4-\log ^2(3)-\log (27)\right )\right ) \int \frac {x}{\log (x)} \, dx-(6 (2+\log (27))) \int \frac {x^2}{\log (x)} \, dx \\ & = 25 x^2+30 \operatorname {ExpIntegralEi}(3 \log (x))+10 \operatorname {ExpIntegralEi}(2 \log (x)) (2-\log (9))-\frac {4 x^4}{\log (x)}+\frac {2 x^2 \left (4-\log ^2(3)-\log (27)\right )}{\log (x)}+\frac {2 x^3 (2+\log (27))}{\log (x)}-2 \int \frac {x^3}{\log ^3(x)} \, dx+16 \text {Subst}\left (\int \frac {e^{4 x}}{x} \, dx,x,\log (x)\right )-(2 (2-\log (9))) \int \frac {x^2}{\log ^3(x)} \, dx-\frac {1}{2} (2-\log (9))^2 \int \frac {x}{\log ^3(x)} \, dx-\left (4 \left (4-\log ^2(3)-\log (27)\right )\right ) \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right )-(6 (2+\log (27))) \text {Subst}\left (\int \frac {e^{3 x}}{x} \, dx,x,\log (x)\right ) \\ & = 25 x^2+30 \operatorname {ExpIntegralEi}(3 \log (x))+16 \operatorname {ExpIntegralEi}(4 \log (x))+10 \operatorname {ExpIntegralEi}(2 \log (x)) (2-\log (9))-4 \operatorname {ExpIntegralEi}(2 \log (x)) \left (4-\log ^2(3)-\log (27)\right )-6 \operatorname {ExpIntegralEi}(3 \log (x)) (2+\log (27))+\frac {x^4}{\log ^2(x)}+\frac {x^3 (2-\log (9))}{\log ^2(x)}+\frac {x^2 (2-\log (9))^2}{4 \log ^2(x)}-\frac {4 x^4}{\log (x)}+\frac {2 x^2 \left (4-\log ^2(3)-\log (27)\right )}{\log (x)}+\frac {2 x^3 (2+\log (27))}{\log (x)}-4 \int \frac {x^3}{\log ^2(x)} \, dx-(3 (2-\log (9))) \int \frac {x^2}{\log ^2(x)} \, dx-\frac {1}{2} (2-\log (9))^2 \int \frac {x}{\log ^2(x)} \, dx \\ & = 25 x^2+30 \operatorname {ExpIntegralEi}(3 \log (x))+16 \operatorname {ExpIntegralEi}(4 \log (x))+10 \operatorname {ExpIntegralEi}(2 \log (x)) (2-\log (9))-4 \operatorname {ExpIntegralEi}(2 \log (x)) \left (4-\log ^2(3)-\log (27)\right )-6 \operatorname {ExpIntegralEi}(3 \log (x)) (2+\log (27))+\frac {x^4}{\log ^2(x)}+\frac {x^3 (2-\log (9))}{\log ^2(x)}+\frac {x^2 (2-\log (9))^2}{4 \log ^2(x)}+\frac {3 x^3 (2-\log (9))}{\log (x)}+\frac {x^2 (2-\log (9))^2}{2 \log (x)}+\frac {2 x^2 \left (4-\log ^2(3)-\log (27)\right )}{\log (x)}+\frac {2 x^3 (2+\log (27))}{\log (x)}-16 \int \frac {x^3}{\log (x)} \, dx-(9 (2-\log (9))) \int \frac {x^2}{\log (x)} \, dx-(2-\log (9))^2 \int \frac {x}{\log (x)} \, dx \\ & = 25 x^2+30 \operatorname {ExpIntegralEi}(3 \log (x))+16 \operatorname {ExpIntegralEi}(4 \log (x))+10 \operatorname {ExpIntegralEi}(2 \log (x)) (2-\log (9))-4 \operatorname {ExpIntegralEi}(2 \log (x)) \left (4-\log ^2(3)-\log (27)\right )-6 \operatorname {ExpIntegralEi}(3 \log (x)) (2+\log (27))+\frac {x^4}{\log ^2(x)}+\frac {x^3 (2-\log (9))}{\log ^2(x)}+\frac {x^2 (2-\log (9))^2}{4 \log ^2(x)}+\frac {3 x^3 (2-\log (9))}{\log (x)}+\frac {x^2 (2-\log (9))^2}{2 \log (x)}+\frac {2 x^2 \left (4-\log ^2(3)-\log (27)\right )}{\log (x)}+\frac {2 x^3 (2+\log (27))}{\log (x)}-16 \text {Subst}\left (\int \frac {e^{4 x}}{x} \, dx,x,\log (x)\right )-(9 (2-\log (9))) \text {Subst}\left (\int \frac {e^{3 x}}{x} \, dx,x,\log (x)\right )-(2-\log (9))^2 \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right ) \\ & = 25 x^2+30 \operatorname {ExpIntegralEi}(3 \log (x))+10 \operatorname {ExpIntegralEi}(2 \log (x)) (2-\log (9))-9 \operatorname {ExpIntegralEi}(3 \log (x)) (2-\log (9))-\operatorname {ExpIntegralEi}(2 \log (x)) (2-\log (9))^2-4 \operatorname {ExpIntegralEi}(2 \log (x)) \left (4-\log ^2(3)-\log (27)\right )-6 \operatorname {ExpIntegralEi}(3 \log (x)) (2+\log (27))+\frac {x^4}{\log ^2(x)}+\frac {x^3 (2-\log (9))}{\log ^2(x)}+\frac {x^2 (2-\log (9))^2}{4 \log ^2(x)}+\frac {3 x^3 (2-\log (9))}{\log (x)}+\frac {x^2 (2-\log (9))^2}{2 \log (x)}+\frac {2 x^2 \left (4-\log ^2(3)-\log (27)\right )}{\log (x)}+\frac {2 x^3 (2+\log (27))}{\log (x)} \\ \end{align*}

Mathematica [B] (veriﬁed)

Leaf count is larger than twice the leaf count of optimal. \(46\) vs. \(2(21)=42\).

Time = 0.58 (sec) , antiderivative size = 46, normalized size of antiderivative = 2.19 \[ \int \frac {-2 x-4 x^2-2 x^3+\left (4 x+4 x^2\right ) \log (3)-2 x \log ^2(3)+\left (-8 x-4 x^2+4 x^3+\left (6 x-6 x^2\right ) \log (3)+2 x \log ^2(3)\right ) \log (x)+\left (20 x+30 x^2-20 x \log (3)\right ) \log ^2(x)+50 x \log ^3(x)}{\log ^3(x)} \, dx=\frac {x^2 \left (1+x^2+\log ^2(3)-x (-2+\log (9))-\log (9)+(10+10 x-\log (59049)) \log (x)+25 \log ^2(x)\right )}{\log ^2(x)} \]

Maple [B] (veriﬁed)

Leaf count of result is larger than twice the leaf count of optimal. \(50\) vs. \(2(21)=42\).

Time = 0.12 (sec) , antiderivative size = 51, normalized size of antiderivative = 2.43


method	result	size

risch	\(25 x^{2}+\frac {x^{2} \left (\ln \left (3\right )^{2}-2 x \ln \left (3\right )-10 \ln \left (3\right ) \ln \left (x \right )+x^{2}+10 x \ln \left (x \right )-2 \ln \left (3\right )+2 x +10 \ln \left (x \right )+1\right )}{\ln \left (x \right )^{2}}\)	\(51\)
norman	\(\frac {x^{4}+\left (-2 \ln \left (3\right )+2\right ) x^{3}+\left (\ln \left (3\right )^{2}-2 \ln \left (3\right )+1\right ) x^{2}+\left (-10 \ln \left (3\right )+10\right ) x^{2} \ln \left (x \right )+25 x^{2} \ln \left (x \right )^{2}+10 x^{3} \ln \left (x \right )}{\ln \left (x \right )^{2}}\)	\(62\)
parallelrisch	\(\frac {x^{2} \ln \left (3\right )^{2}-2 x^{3} \ln \left (3\right )-10 x^{2} \ln \left (3\right ) \ln \left (x \right )+x^{4}+10 x^{3} \ln \left (x \right )+25 x^{2} \ln \left (x \right )^{2}-2 x^{2} \ln \left (3\right )+2 x^{3}+10 x^{2} \ln \left (x \right )+x^{2}}{\ln \left (x \right )^{2}}\)	\(72\)
default	\(20 \ln \left (3\right ) \operatorname {Ei}_{1}\left (-2 \ln \left (x \right )\right )+\frac {x^{2}}{\ln \left (x \right )^{2}}+\frac {10 x^{3}}{\ln \left (x \right )}+\frac {x^{4}}{\ln \left (x \right )^{2}}+\frac {2 x^{3}}{\ln \left (x \right )^{2}}+\frac {10 x^{2}}{\ln \left (x \right )}+25 x^{2}+4 \ln \left (3\right ) \left (-\frac {x^{2}}{2 \ln \left (x \right )^{2}}-\frac {x^{2}}{\ln \left (x \right )}-2 \,\operatorname {Ei}_{1}\left (-2 \ln \left (x \right )\right )\right )+4 \ln \left (3\right ) \left (-\frac {x^{3}}{2 \ln \left (x \right )^{2}}-\frac {3 x^{3}}{2 \ln \left (x \right )}-\frac {9 \,\operatorname {Ei}_{1}\left (-3 \ln \left (x \right )\right )}{2}\right )-2 \ln \left (3\right )^{2} \left (-\frac {x^{2}}{2 \ln \left (x \right )^{2}}-\frac {x^{2}}{\ln \left (x \right )}-2 \,\operatorname {Ei}_{1}\left (-2 \ln \left (x \right )\right )\right )+2 \ln \left (3\right )^{2} \left (-\frac {x^{2}}{\ln \left (x \right )}-2 \,\operatorname {Ei}_{1}\left (-2 \ln \left (x \right )\right )\right )-6 \ln \left (3\right ) \left (-\frac {x^{3}}{\ln \left (x \right )}-3 \,\operatorname {Ei}_{1}\left (-3 \ln \left (x \right )\right )\right )+6 \ln \left (3\right ) \left (-\frac {x^{2}}{\ln \left (x \right )}-2 \,\operatorname {Ei}_{1}\left (-2 \ln \left (x \right )\right )\right )\)	\(223\)
parts	\(20 \ln \left (3\right ) \operatorname {Ei}_{1}\left (-2 \ln \left (x \right )\right )+\frac {x^{2}}{\ln \left (x \right )^{2}}+\frac {10 x^{3}}{\ln \left (x \right )}+\frac {x^{4}}{\ln \left (x \right )^{2}}+\frac {2 x^{3}}{\ln \left (x \right )^{2}}+\frac {10 x^{2}}{\ln \left (x \right )}+25 x^{2}+4 \ln \left (3\right ) \left (-\frac {x^{2}}{2 \ln \left (x \right )^{2}}-\frac {x^{2}}{\ln \left (x \right )}-2 \,\operatorname {Ei}_{1}\left (-2 \ln \left (x \right )\right )\right )+4 \ln \left (3\right ) \left (-\frac {x^{3}}{2 \ln \left (x \right )^{2}}-\frac {3 x^{3}}{2 \ln \left (x \right )}-\frac {9 \,\operatorname {Ei}_{1}\left (-3 \ln \left (x \right )\right )}{2}\right )-2 \ln \left (3\right )^{2} \left (-\frac {x^{2}}{2 \ln \left (x \right )^{2}}-\frac {x^{2}}{\ln \left (x \right )}-2 \,\operatorname {Ei}_{1}\left (-2 \ln \left (x \right )\right )\right )+2 \ln \left (3\right )^{2} \left (-\frac {x^{2}}{\ln \left (x \right )}-2 \,\operatorname {Ei}_{1}\left (-2 \ln \left (x \right )\right )\right )-6 \ln \left (3\right ) \left (-\frac {x^{3}}{\ln \left (x \right )}-3 \,\operatorname {Ei}_{1}\left (-3 \ln \left (x \right )\right )\right )+6 \ln \left (3\right ) \left (-\frac {x^{2}}{\ln \left (x \right )}-2 \,\operatorname {Ei}_{1}\left (-2 \ln \left (x \right )\right )\right )\)	\(223\)

Fricas [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (20) = 40\).

Time = 0.27 (sec) , antiderivative size = 63, normalized size of antiderivative = 3.00 \[ \int \frac {-2 x-4 x^2-2 x^3+\left (4 x+4 x^2\right ) \log (3)-2 x \log ^2(3)+\left (-8 x-4 x^2+4 x^3+\left (6 x-6 x^2\right ) \log (3)+2 x \log ^2(3)\right ) \log (x)+\left (20 x+30 x^2-20 x \log (3)\right ) \log ^2(x)+50 x \log ^3(x)}{\log ^3(x)} \, dx=\frac {x^{4} + x^{2} \log \left (3\right )^{2} + 25 \, x^{2} \log \left (x\right )^{2} + 2 \, x^{3} + x^{2} - 2 \, {\left (x^{3} + x^{2}\right )} \log \left (3\right ) + 10 \, {\left (x^{3} - x^{2} \log \left (3\right ) + x^{2}\right )} \log \left (x\right )}{\log \left (x\right )^{2}} \]

Sympy [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 68 vs. \(2 (17) = 34\).

Time = 0.06 (sec) , antiderivative size = 68, normalized size of antiderivative = 3.24 \[ \int \frac {-2 x-4 x^2-2 x^3+\left (4 x+4 x^2\right ) \log (3)-2 x \log ^2(3)+\left (-8 x-4 x^2+4 x^3+\left (6 x-6 x^2\right ) \log (3)+2 x \log ^2(3)\right ) \log (x)+\left (20 x+30 x^2-20 x \log (3)\right ) \log ^2(x)+50 x \log ^3(x)}{\log ^3(x)} \, dx=25 x^{2} + \frac {x^{4} - 2 x^{3} \log {\left (3 \right )} + 2 x^{3} - 2 x^{2} \log {\left (3 \right )} + x^{2} + x^{2} \log {\left (3 \right )}^{2} + \left (10 x^{3} - 10 x^{2} \log {\left (3 \right )} + 10 x^{2}\right ) \log {\left (x \right )}}{\log {\left (x \right )}^{2}} \]

Maxima [C] (veriﬁcation not implemented)

Time = 0.25 (sec) , antiderivative size = 141, normalized size of antiderivative = 6.71 \[ \int \frac {-2 x-4 x^2-2 x^3+\left (4 x+4 x^2\right ) \log (3)-2 x \log ^2(3)+\left (-8 x-4 x^2+4 x^3+\left (6 x-6 x^2\right ) \log (3)+2 x \log ^2(3)\right ) \log (x)+\left (20 x+30 x^2-20 x \log (3)\right ) \log ^2(x)+50 x \log ^3(x)}{\log ^3(x)} \, dx=4 \, \Gamma \left (-1, -2 \, \log \left (x\right )\right ) \log \left (3\right )^{2} + 8 \, \Gamma \left (-2, -2 \, \log \left (x\right )\right ) \log \left (3\right )^{2} + 25 \, x^{2} - 20 \, {\rm Ei}\left (2 \, \log \left (x\right )\right ) \log \left (3\right ) + 12 \, \Gamma \left (-1, -2 \, \log \left (x\right )\right ) \log \left (3\right ) - 18 \, \Gamma \left (-1, -3 \, \log \left (x\right )\right ) \log \left (3\right ) - 16 \, \Gamma \left (-2, -2 \, \log \left (x\right )\right ) \log \left (3\right ) - 36 \, \Gamma \left (-2, -3 \, \log \left (x\right )\right ) \log \left (3\right ) + 30 \, {\rm Ei}\left (3 \, \log \left (x\right )\right ) + 20 \, {\rm Ei}\left (2 \, \log \left (x\right )\right ) - 16 \, \Gamma \left (-1, -2 \, \log \left (x\right )\right ) - 12 \, \Gamma \left (-1, -3 \, \log \left (x\right )\right ) + 16 \, \Gamma \left (-1, -4 \, \log \left (x\right )\right ) + 8 \, \Gamma \left (-2, -2 \, \log \left (x\right )\right ) + 36 \, \Gamma \left (-2, -3 \, \log \left (x\right )\right ) + 32 \, \Gamma \left (-2, -4 \, \log \left (x\right )\right ) \]

Giac [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 94 vs. \(2 (20) = 40\).

Time = 0.26 (sec) , antiderivative size = 94, normalized size of antiderivative = 4.48 \[ \int \frac {-2 x-4 x^2-2 x^3+\left (4 x+4 x^2\right ) \log (3)-2 x \log ^2(3)+\left (-8 x-4 x^2+4 x^3+\left (6 x-6 x^2\right ) \log (3)+2 x \log ^2(3)\right ) \log (x)+\left (20 x+30 x^2-20 x \log (3)\right ) \log ^2(x)+50 x \log ^3(x)}{\log ^3(x)} \, dx=25 \, x^{2} + \frac {x^{4}}{\log \left (x\right )^{2}} - \frac {2 \, x^{3} \log \left (3\right )}{\log \left (x\right )^{2}} + \frac {x^{2} \log \left (3\right )^{2}}{\log \left (x\right )^{2}} + \frac {10 \, x^{3}}{\log \left (x\right )} - \frac {10 \, x^{2} \log \left (3\right )}{\log \left (x\right )} + \frac {2 \, x^{3}}{\log \left (x\right )^{2}} - \frac {2 \, x^{2} \log \left (3\right )}{\log \left (x\right )^{2}} + \frac {10 \, x^{2}}{\log \left (x\right )} + \frac {x^{2}}{\log \left (x\right )^{2}} \]

Mupad [B] (veriﬁcation not implemented)

Time = 14.02 (sec) , antiderivative size = 63, normalized size of antiderivative = 3.00 \[ \int \frac {-2 x-4 x^2-2 x^3+\left (4 x+4 x^2\right ) \log (3)-2 x \log ^2(3)+\left (-8 x-4 x^2+4 x^3+\left (6 x-6 x^2\right ) \log (3)+2 x \log ^2(3)\right ) \log (x)+\left (20 x+30 x^2-20 x \log (3)\right ) \log ^2(x)+50 x \log ^3(x)}{\log ^3(x)} \, dx=25\,x^2-\frac {x^4\,\left (\ln \left (9\right )-2\right )-x^3\,\left ({\ln \left (3\right )}^2-\ln \left (9\right )+1\right )+\ln \left (x\right )\,\left (x^3\,\left (10\,\ln \left (3\right )-10\right )-10\,x^4\right )-x^5}{x\,{\ln \left (x\right )}^2} \]

\(\int \frac {-2 x-4 x^2-2 x^3+(4 x+4 x^2) \log (3)-2 x \log ^2(3)+(-8 x-4 x^2+4 x^3+(6 x-6 x^2) \log (3)+2 x \log ^2(3)) \log (x)+(20 x+30 x^2-20 x \log (3)) \log ^2(x)+50 x \log ^3(x)}{\log ^3(x)} \, dx\) [8736]

Optimal result