3.3.0 ∫ −663552x−921600x2−467456x3−102400x4−8192x5+(664704x+1383200x2+935040x3+256000x4+24576x5+(1152+800x+128x2) log(5)) log(x)+(−2304x−2400x2−512x3+(−1152−1600x−384x2) log(5)) log2(x)+(2x+2 log(5)) log3(x) log3 (x) dx [207]

Integrand size = 114, antiderivative size = 22 \[ \int \frac {-663552 x-921600 x^2-467456 x^3-102400 x^4-8192 x^5+\left (664704 x+1383200 x^2+935040 x^3+256000 x^4+24576 x^5+\left (1152+800 x+128 x^2\right ) \log (5)\right ) \log (x)+\left (-2304 x-2400 x^2-512 x^3+\left (-1152-1600 x-384 x^2\right ) \log (5)\right ) \log ^2(x)+(2 x+2 \log (5)) \log ^3(x)}{\log ^3(x)} \, dx=\left (x+\log (5)-\frac {16 x \left (x+(6+2 x)^2\right )}{\log (x)}\right )^2 \]

Rubi [C] (veriﬁed)

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

Time = 1.00 (sec) , antiderivative size = 180, normalized size of antiderivative = 8.18, number of steps used = 54, number of rules used = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.079, Rules used = {6820, 12, 6874, 2403, 2343, 2346, 2209, 2334, 2335} \[ \int \frac {-663552 x-921600 x^2-467456 x^3-102400 x^4-8192 x^5+\left (664704 x+1383200 x^2+935040 x^3+256000 x^4+24576 x^5+\left (1152+800 x+128 x^2\right ) \log (5)\right ) \log (x)+\left (-2304 x-2400 x^2-512 x^3+\left (-1152-1600 x-384 x^2\right ) \log (5)\right ) \log ^2(x)+(2 x+2 \log (5)) \log ^3(x)}{\log ^3(x)} \, dx=-1327104 \operatorname {ExpIntegralEi}(2 \log (x))-4147200 \operatorname {ExpIntegralEi}(3 \log (x))+96 (43225+\log (625)) \operatorname {ExpIntegralEi}(3 \log (x))-96 (25+\log (625)) \operatorname {ExpIntegralEi}(3 \log (x))+64 (20772+25 \log (5)) \operatorname {ExpIntegralEi}(2 \log (x))-64 (36+25 \log (5)) \operatorname {ExpIntegralEi}(2 \log (x))+\frac {4096 x^6}{\log ^2(x)}+\frac {51200 x^5}{\log ^2(x)}+\frac {233728 x^4}{\log ^2(x)}-\frac {128 x^4}{\log (x)}+\frac {460800 x^3}{\log ^2(x)}-\frac {32 x^3 (43225+\log (625))}{\log (x)}+\frac {1382400 x^3}{\log (x)}+x^2+\frac {331776 x^2}{\log ^2(x)}-\frac {32 x^2 (20772+25 \log (5))}{\log (x)}+\frac {663552 x^2}{\log (x)}-\frac {1152 x \log (5)}{\log (x)}+2 x \log (5) \]

Rubi steps \begin{align*} \text {integral}& = \int \frac {2 \left (16 x \left (36+25 x+4 x^2\right )-(x+\log (5)) \log (x)\right ) \left (-16 \left (36+25 x+4 x^2\right )+32 \left (18+25 x+6 x^2\right ) \log (x)-\log ^2(x)\right )}{\log ^3(x)} \, dx \\ & = 2 \int \frac {\left (16 x \left (36+25 x+4 x^2\right )-(x+\log (5)) \log (x)\right ) \left (-16 \left (36+25 x+4 x^2\right )+32 \left (18+25 x+6 x^2\right ) \log (x)-\log ^2(x)\right )}{\log ^3(x)} \, dx \\ & = 2 \int \left (x+\log (5)-\frac {256 x (4+x)^2 (9+4 x)^2}{\log ^3(x)}+\frac {16 \left (36+25 x+4 x^2\right ) \left (577 x+800 x^2+192 x^3+\log (5)\right )}{\log ^2(x)}+\frac {16 \left (-16 x^3-36 \log (5)-2 x (36+25 \log (5))-3 x^2 (25+\log (625))\right )}{\log (x)}\right ) \, dx \\ & = x^2+2 x \log (5)+32 \int \frac {\left (36+25 x+4 x^2\right ) \left (577 x+800 x^2+192 x^3+\log (5)\right )}{\log ^2(x)} \, dx+32 \int \frac {-16 x^3-36 \log (5)-2 x (36+25 \log (5))-3 x^2 (25+\log (625))}{\log (x)} \, dx-512 \int \frac {x (4+x)^2 (9+4 x)^2}{\log ^3(x)} \, dx \\ & = x^2+2 x \log (5)+32 \int \left (\frac {29220 x^3}{\log ^2(x)}+\frac {8000 x^4}{\log ^2(x)}+\frac {768 x^5}{\log ^2(x)}+\frac {36 \log (5)}{\log ^2(x)}+\frac {x (20772+25 \log (5))}{\log ^2(x)}+\frac {x^2 (43225+\log (625))}{\log ^2(x)}\right ) \, dx+32 \int \left (-\frac {16 x^3}{\log (x)}-\frac {36 \log (5)}{\log (x)}-\frac {2 x (36+25 \log (5))}{\log (x)}-\frac {3 x^2 (25+\log (625))}{\log (x)}\right ) \, dx-512 \int \left (\frac {1296 x}{\log ^3(x)}+\frac {1800 x^2}{\log ^3(x)}+\frac {913 x^3}{\log ^3(x)}+\frac {200 x^4}{\log ^3(x)}+\frac {16 x^5}{\log ^3(x)}\right ) \, dx \\ & = x^2+2 x \log (5)-512 \int \frac {x^3}{\log (x)} \, dx-8192 \int \frac {x^5}{\log ^3(x)} \, dx+24576 \int \frac {x^5}{\log ^2(x)} \, dx-102400 \int \frac {x^4}{\log ^3(x)} \, dx+256000 \int \frac {x^4}{\log ^2(x)} \, dx-467456 \int \frac {x^3}{\log ^3(x)} \, dx-663552 \int \frac {x}{\log ^3(x)} \, dx-921600 \int \frac {x^2}{\log ^3(x)} \, dx+935040 \int \frac {x^3}{\log ^2(x)} \, dx+(1152 \log (5)) \int \frac {1}{\log ^2(x)} \, dx-(1152 \log (5)) \int \frac {1}{\log (x)} \, dx-(64 (36+25 \log (5))) \int \frac {x}{\log (x)} \, dx+(32 (20772+25 \log (5))) \int \frac {x}{\log ^2(x)} \, dx-(96 (25+\log (625))) \int \frac {x^2}{\log (x)} \, dx+(32 (43225+\log (625))) \int \frac {x^2}{\log ^2(x)} \, dx \\ & = x^2+2 x \log (5)+\frac {331776 x^2}{\log ^2(x)}+\frac {460800 x^3}{\log ^2(x)}+\frac {233728 x^4}{\log ^2(x)}+\frac {51200 x^5}{\log ^2(x)}+\frac {4096 x^6}{\log ^2(x)}-\frac {935040 x^4}{\log (x)}-\frac {256000 x^5}{\log (x)}-\frac {24576 x^6}{\log (x)}-\frac {1152 x \log (5)}{\log (x)}-\frac {32 x^2 (20772+25 \log (5))}{\log (x)}-\frac {32 x^3 (43225+\log (625))}{\log (x)}-1152 \log (5) \operatorname {LogIntegral}(x)-512 \text {Subst}\left (\int \frac {e^{4 x}}{x} \, dx,x,\log (x)\right )-24576 \int \frac {x^5}{\log ^2(x)} \, dx+147456 \int \frac {x^5}{\log (x)} \, dx-256000 \int \frac {x^4}{\log ^2(x)} \, dx-663552 \int \frac {x}{\log ^2(x)} \, dx-934912 \int \frac {x^3}{\log ^2(x)} \, dx+1280000 \int \frac {x^4}{\log (x)} \, dx-1382400 \int \frac {x^2}{\log ^2(x)} \, dx+3740160 \int \frac {x^3}{\log (x)} \, dx+(1152 \log (5)) \int \frac {1}{\log (x)} \, dx-(64 (36+25 \log (5))) \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right )+(64 (20772+25 \log (5))) \int \frac {x}{\log (x)} \, dx-(96 (25+\log (625))) \text {Subst}\left (\int \frac {e^{3 x}}{x} \, dx,x,\log (x)\right )+(96 (43225+\log (625))) \int \frac {x^2}{\log (x)} \, dx \\ & = x^2-512 \operatorname {ExpIntegralEi}(4 \log (x))+2 x \log (5)-64 \operatorname {ExpIntegralEi}(2 \log (x)) (36+25 \log (5))-96 \operatorname {ExpIntegralEi}(3 \log (x)) (25+\log (625))+\frac {331776 x^2}{\log ^2(x)}+\frac {460800 x^3}{\log ^2(x)}+\frac {233728 x^4}{\log ^2(x)}+\frac {51200 x^5}{\log ^2(x)}+\frac {4096 x^6}{\log ^2(x)}+\frac {663552 x^2}{\log (x)}+\frac {1382400 x^3}{\log (x)}-\frac {128 x^4}{\log (x)}-\frac {1152 x \log (5)}{\log (x)}-\frac {32 x^2 (20772+25 \log (5))}{\log (x)}-\frac {32 x^3 (43225+\log (625))}{\log (x)}-147456 \int \frac {x^5}{\log (x)} \, dx+147456 \text {Subst}\left (\int \frac {e^{6 x}}{x} \, dx,x,\log (x)\right )-1280000 \int \frac {x^4}{\log (x)} \, dx+1280000 \text {Subst}\left (\int \frac {e^{5 x}}{x} \, dx,x,\log (x)\right )-1327104 \int \frac {x}{\log (x)} \, dx-3739648 \int \frac {x^3}{\log (x)} \, dx+3740160 \text {Subst}\left (\int \frac {e^{4 x}}{x} \, dx,x,\log (x)\right )-4147200 \int \frac {x^2}{\log (x)} \, dx+(64 (20772+25 \log (5))) \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right )+(96 (43225+\log (625))) \text {Subst}\left (\int \frac {e^{3 x}}{x} \, dx,x,\log (x)\right ) \\ & = x^2+3739648 \operatorname {ExpIntegralEi}(4 \log (x))+1280000 \operatorname {ExpIntegralEi}(5 \log (x))+147456 \operatorname {ExpIntegralEi}(6 \log (x))+2 x \log (5)-64 \operatorname {ExpIntegralEi}(2 \log (x)) (36+25 \log (5))+64 \operatorname {ExpIntegralEi}(2 \log (x)) (20772+25 \log (5))-96 \operatorname {ExpIntegralEi}(3 \log (x)) (25+\log (625))+96 \operatorname {ExpIntegralEi}(3 \log (x)) (43225+\log (625))+\frac {331776 x^2}{\log ^2(x)}+\frac {460800 x^3}{\log ^2(x)}+\frac {233728 x^4}{\log ^2(x)}+\frac {51200 x^5}{\log ^2(x)}+\frac {4096 x^6}{\log ^2(x)}+\frac {663552 x^2}{\log (x)}+\frac {1382400 x^3}{\log (x)}-\frac {128 x^4}{\log (x)}-\frac {1152 x \log (5)}{\log (x)}-\frac {32 x^2 (20772+25 \log (5))}{\log (x)}-\frac {32 x^3 (43225+\log (625))}{\log (x)}-147456 \text {Subst}\left (\int \frac {e^{6 x}}{x} \, dx,x,\log (x)\right )-1280000 \text {Subst}\left (\int \frac {e^{5 x}}{x} \, dx,x,\log (x)\right )-1327104 \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right )-3739648 \text {Subst}\left (\int \frac {e^{4 x}}{x} \, dx,x,\log (x)\right )-4147200 \text {Subst}\left (\int \frac {e^{3 x}}{x} \, dx,x,\log (x)\right ) \\ & = x^2-1327104 \operatorname {ExpIntegralEi}(2 \log (x))-4147200 \operatorname {ExpIntegralEi}(3 \log (x))+2 x \log (5)-64 \operatorname {ExpIntegralEi}(2 \log (x)) (36+25 \log (5))+64 \operatorname {ExpIntegralEi}(2 \log (x)) (20772+25 \log (5))-96 \operatorname {ExpIntegralEi}(3 \log (x)) (25+\log (625))+96 \operatorname {ExpIntegralEi}(3 \log (x)) (43225+\log (625))+\frac {331776 x^2}{\log ^2(x)}+\frac {460800 x^3}{\log ^2(x)}+\frac {233728 x^4}{\log ^2(x)}+\frac {51200 x^5}{\log ^2(x)}+\frac {4096 x^6}{\log ^2(x)}+\frac {663552 x^2}{\log (x)}+\frac {1382400 x^3}{\log (x)}-\frac {128 x^4}{\log (x)}-\frac {1152 x \log (5)}{\log (x)}-\frac {32 x^2 (20772+25 \log (5))}{\log (x)}-\frac {32 x^3 (43225+\log (625))}{\log (x)} \\ \end{align*}

Mathematica [A] (veriﬁed)

Time = 2.08 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.91 \[ \int \frac {-663552 x-921600 x^2-467456 x^3-102400 x^4-8192 x^5+\left (664704 x+1383200 x^2+935040 x^3+256000 x^4+24576 x^5+\left (1152+800 x+128 x^2\right ) \log (5)\right ) \log (x)+\left (-2304 x-2400 x^2-512 x^3+\left (-1152-1600 x-384 x^2\right ) \log (5)\right ) \log ^2(x)+(2 x+2 \log (5)) \log ^3(x)}{\log ^3(x)} \, dx=\frac {x \left (576+400 x+64 x^2-\log (x)\right ) \left (16 x \left (36+25 x+4 x^2\right )-(x+\log (25)) \log (x)\right )}{\log ^2(x)} \]

Maple [B] (veriﬁed)

Leaf count of result is larger than twice the leaf count of optimal. \(81\) vs. \(2(26)=52\).

Time = 0.11 (sec) , antiderivative size = 82, normalized size of antiderivative = 3.73


method	result	size

risch	\(2 x \ln \left (5\right )+x^{2}-\frac {32 x \left (-128 x^{5}+4 x^{2} \ln \left (5\right ) \ln \left (x \right )-1600 x^{4}+4 x^{3} \ln \left (x \right )+25 x \ln \left (5\right ) \ln \left (x \right )-7304 x^{3}+25 x^{2} \ln \left (x \right )+36 \ln \left (5\right ) \ln \left (x \right )-14400 x^{2}+36 x \ln \left (x \right )-10368 x \right )}{\ln \left (x \right )^{2}}\)	\(82\)
norman	\(\frac {x^{2} \ln \left (x \right )^{2}+\left (-1152-800 \ln \left (5\right )\right ) x^{2} \ln \left (x \right )+\left (-800-128 \ln \left (5\right )\right ) x^{3} \ln \left (x \right )+331776 x^{2}+460800 x^{3}+233728 x^{4}+51200 x^{5}+4096 x^{6}-128 x^{4} \ln \left (x \right )-1152 x \ln \left (5\right ) \ln \left (x \right )+2 \ln \left (x \right )^{2} \ln \left (5\right ) x}{\ln \left (x \right )^{2}}\)	\(87\)
parallelrisch	\(-\frac {-4096 x^{6}+128 \ln \left (5\right ) x^{3} \ln \left (x \right )-51200 x^{5}+128 x^{4} \ln \left (x \right )+800 x^{2} \ln \left (5\right ) \ln \left (x \right )-2 \ln \left (x \right )^{2} \ln \left (5\right ) x -233728 x^{4}+800 x^{3} \ln \left (x \right )-x^{2} \ln \left (x \right )^{2}+1152 x \ln \left (5\right ) \ln \left (x \right )-460800 x^{3}+1152 x^{2} \ln \left (x \right )-331776 x^{2}}{\ln \left (x \right )^{2}}\)	\(97\)
default	\(\frac {331776 x^{2}}{\ln \left (x \right )^{2}}-\frac {128 x^{4}}{\ln \left (x \right )}+2 x \ln \left (5\right )+1152 \ln \left (5\right ) \left (-\frac {x}{\ln \left (x \right )}-\operatorname {Ei}_{1}\left (-\ln \left (x \right )\right )\right )+800 \ln \left (5\right ) \left (-\frac {x^{2}}{\ln \left (x \right )}-2 \,\operatorname {Ei}_{1}\left (-2 \ln \left (x \right )\right )\right )+128 \ln \left (5\right ) \left (-\frac {x^{3}}{\ln \left (x \right )}-3 \,\operatorname {Ei}_{1}\left (-3 \ln \left (x \right )\right )\right )+1152 \ln \left (5\right ) \operatorname {Ei}_{1}\left (-\ln \left (x \right )\right )+\frac {4096 x^{6}}{\ln \left (x \right )^{2}}+1600 \ln \left (5\right ) \operatorname {Ei}_{1}\left (-2 \ln \left (x \right )\right )+384 \ln \left (5\right ) \operatorname {Ei}_{1}\left (-3 \ln \left (x \right )\right )+\frac {51200 x^{5}}{\ln \left (x \right )^{2}}-\frac {800 x^{3}}{\ln \left (x \right )}+\frac {233728 x^{4}}{\ln \left (x \right )^{2}}+\frac {460800 x^{3}}{\ln \left (x \right )^{2}}-\frac {1152 x^{2}}{\ln \left (x \right )}+x^{2}\)	\(176\)
parts	\(\frac {331776 x^{2}}{\ln \left (x \right )^{2}}-\frac {128 x^{4}}{\ln \left (x \right )}+2 x \ln \left (5\right )+1152 \ln \left (5\right ) \left (-\frac {x}{\ln \left (x \right )}-\operatorname {Ei}_{1}\left (-\ln \left (x \right )\right )\right )+800 \ln \left (5\right ) \left (-\frac {x^{2}}{\ln \left (x \right )}-2 \,\operatorname {Ei}_{1}\left (-2 \ln \left (x \right )\right )\right )+128 \ln \left (5\right ) \left (-\frac {x^{3}}{\ln \left (x \right )}-3 \,\operatorname {Ei}_{1}\left (-3 \ln \left (x \right )\right )\right )+1152 \ln \left (5\right ) \operatorname {Ei}_{1}\left (-\ln \left (x \right )\right )+\frac {4096 x^{6}}{\ln \left (x \right )^{2}}+1600 \ln \left (5\right ) \operatorname {Ei}_{1}\left (-2 \ln \left (x \right )\right )+384 \ln \left (5\right ) \operatorname {Ei}_{1}\left (-3 \ln \left (x \right )\right )+\frac {51200 x^{5}}{\ln \left (x \right )^{2}}-\frac {800 x^{3}}{\ln \left (x \right )}+\frac {233728 x^{4}}{\ln \left (x \right )^{2}}+\frac {460800 x^{3}}{\ln \left (x \right )^{2}}-\frac {1152 x^{2}}{\ln \left (x \right )}+x^{2}\)	\(176\)

Fricas [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 82 vs. \(2 (22) = 44\).

Time = 0.25 (sec) , antiderivative size = 82, normalized size of antiderivative = 3.73 \[ \int \frac {-663552 x-921600 x^2-467456 x^3-102400 x^4-8192 x^5+\left (664704 x+1383200 x^2+935040 x^3+256000 x^4+24576 x^5+\left (1152+800 x+128 x^2\right ) \log (5)\right ) \log (x)+\left (-2304 x-2400 x^2-512 x^3+\left (-1152-1600 x-384 x^2\right ) \log (5)\right ) \log ^2(x)+(2 x+2 \log (5)) \log ^3(x)}{\log ^3(x)} \, dx=\frac {4096 \, x^{6} + 51200 \, x^{5} + 233728 \, x^{4} + 460800 \, x^{3} + {\left (x^{2} + 2 \, x \log \left (5\right )\right )} \log \left (x\right )^{2} + 331776 \, x^{2} - 32 \, {\left (4 \, x^{4} + 25 \, x^{3} + 36 \, x^{2} + {\left (4 \, x^{3} + 25 \, x^{2} + 36 \, x\right )} \log \left (5\right )\right )} \log \left (x\right )}{\log \left (x\right )^{2}} \]

Sympy [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 83 vs. \(2 (22) = 44\).

Time = 0.06 (sec) , antiderivative size = 83, normalized size of antiderivative = 3.77 \[ \int \frac {-663552 x-921600 x^2-467456 x^3-102400 x^4-8192 x^5+\left (664704 x+1383200 x^2+935040 x^3+256000 x^4+24576 x^5+\left (1152+800 x+128 x^2\right ) \log (5)\right ) \log (x)+\left (-2304 x-2400 x^2-512 x^3+\left (-1152-1600 x-384 x^2\right ) \log (5)\right ) \log ^2(x)+(2 x+2 \log (5)) \log ^3(x)}{\log ^3(x)} \, dx=x^{2} + 2 x \log {\left (5 \right )} + \frac {4096 x^{6} + 51200 x^{5} + 233728 x^{4} + 460800 x^{3} + 331776 x^{2} + \left (- 128 x^{4} - 800 x^{3} - 128 x^{3} \log {\left (5 \right )} - 800 x^{2} \log {\left (5 \right )} - 1152 x^{2} - 1152 x \log {\left (5 \right )}\right ) \log {\left (x \right )}}{\log {\left (x \right )}^{2}} \]

Maxima [C] (veriﬁcation not implemented)

Time = 0.25 (sec) , antiderivative size = 165, normalized size of antiderivative = 7.50 \[ \int \frac {-663552 x-921600 x^2-467456 x^3-102400 x^4-8192 x^5+\left (664704 x+1383200 x^2+935040 x^3+256000 x^4+24576 x^5+\left (1152+800 x+128 x^2\right ) \log (5)\right ) \log (x)+\left (-2304 x-2400 x^2-512 x^3+\left (-1152-1600 x-384 x^2\right ) \log (5)\right ) \log ^2(x)+(2 x+2 \log (5)) \log ^3(x)}{\log ^3(x)} \, dx=x^{2} + 2 \, x \log \left (5\right ) - 384 \, {\rm Ei}\left (3 \, \log \left (x\right )\right ) \log \left (5\right ) - 1600 \, {\rm Ei}\left (2 \, \log \left (x\right )\right ) \log \left (5\right ) - 1152 \, {\rm Ei}\left (\log \left (x\right )\right ) \log \left (5\right ) + 1152 \, \Gamma \left (-1, -\log \left (x\right )\right ) \log \left (5\right ) + 1600 \, \Gamma \left (-1, -2 \, \log \left (x\right )\right ) \log \left (5\right ) + 384 \, \Gamma \left (-1, -3 \, \log \left (x\right )\right ) \log \left (5\right ) - 512 \, {\rm Ei}\left (4 \, \log \left (x\right )\right ) - 2400 \, {\rm Ei}\left (3 \, \log \left (x\right )\right ) - 2304 \, {\rm Ei}\left (2 \, \log \left (x\right )\right ) + 1329408 \, \Gamma \left (-1, -2 \, \log \left (x\right )\right ) + 4149600 \, \Gamma \left (-1, -3 \, \log \left (x\right )\right ) + 3740160 \, \Gamma \left (-1, -4 \, \log \left (x\right )\right ) + 1280000 \, \Gamma \left (-1, -5 \, \log \left (x\right )\right ) + 147456 \, \Gamma \left (-1, -6 \, \log \left (x\right )\right ) + 2654208 \, \Gamma \left (-2, -2 \, \log \left (x\right )\right ) + 8294400 \, \Gamma \left (-2, -3 \, \log \left (x\right )\right ) + 7479296 \, \Gamma \left (-2, -4 \, \log \left (x\right )\right ) + 2560000 \, \Gamma \left (-2, -5 \, \log \left (x\right )\right ) + 294912 \, \Gamma \left (-2, -6 \, \log \left (x\right )\right ) \]

Giac [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 112 vs. \(2 (22) = 44\).

Time = 0.26 (sec) , antiderivative size = 112, normalized size of antiderivative = 5.09 \[ \int \frac {-663552 x-921600 x^2-467456 x^3-102400 x^4-8192 x^5+\left (664704 x+1383200 x^2+935040 x^3+256000 x^4+24576 x^5+\left (1152+800 x+128 x^2\right ) \log (5)\right ) \log (x)+\left (-2304 x-2400 x^2-512 x^3+\left (-1152-1600 x-384 x^2\right ) \log (5)\right ) \log ^2(x)+(2 x+2 \log (5)) \log ^3(x)}{\log ^3(x)} \, dx=\frac {4096 \, x^{6}}{\log \left (x\right )^{2}} + \frac {51200 \, x^{5}}{\log \left (x\right )^{2}} - \frac {128 \, x^{4}}{\log \left (x\right )} - \frac {128 \, x^{3} \log \left (5\right )}{\log \left (x\right )} + x^{2} + 2 \, x \log \left (5\right ) + \frac {233728 \, x^{4}}{\log \left (x\right )^{2}} - \frac {800 \, x^{3}}{\log \left (x\right )} - \frac {800 \, x^{2} \log \left (5\right )}{\log \left (x\right )} + \frac {460800 \, x^{3}}{\log \left (x\right )^{2}} - \frac {1152 \, x^{2}}{\log \left (x\right )} - \frac {1152 \, x \log \left (5\right )}{\log \left (x\right )} + \frac {331776 \, x^{2}}{\log \left (x\right )^{2}} \]

Mupad [B] (veriﬁcation not implemented)

Time = 8.08 (sec) , antiderivative size = 74, normalized size of antiderivative = 3.36 \[ \int \frac {-663552 x-921600 x^2-467456 x^3-102400 x^4-8192 x^5+\left (664704 x+1383200 x^2+935040 x^3+256000 x^4+24576 x^5+\left (1152+800 x+128 x^2\right ) \log (5)\right ) \log (x)+\left (-2304 x-2400 x^2-512 x^3+\left (-1152-1600 x-384 x^2\right ) \log (5)\right ) \log ^2(x)+(2 x+2 \log (5)) \log ^3(x)}{\log ^3(x)} \, dx=\frac {x\,\left (4096\,x^5+51200\,x^4+233728\,x^3+460800\,x^2+331776\,x\right )-x\,\ln \left (x\right )\,\left (1152\,x+1152\,\ln \left (5\right )+800\,x\,\ln \left (5\right )+128\,x^2\,\ln \left (5\right )+800\,x^2+128\,x^3\right )}{{\ln \left (x\right )}^2}+x\,\left (x+\ln \left (25\right )\right ) \]

\(\int \frac {-663552 x-921600 x^2-467456 x^3-102400 x^4-8192 x^5+(664704 x+1383200 x^2+935040 x^3+256000 x^4+24576 x^5+(1152+800 x+128 x^2) \log (5)) \log (x)+(-2304 x-2400 x^2-512 x^3+(-1152-1600 x-384 x^2) \log (5)) \log ^2(x)+(2 x+2 \log (5)) \log ^3(x)}{\log ^3(x)} \, dx\) [207]

Optimal result