Integrand size = 114, antiderivative size = 22 \[ \int \frac {-663552 x-921600 x^2-467456 x^3-102400 x^4-8192 x^5+\left (664704 x+1383200 x^2+935040 x^3+256000 x^4+24576 x^5+\left (1152+800 x+128 x^2\right ) \log (5)\right ) \log (x)+\left (-2304 x-2400 x^2-512 x^3+\left (-1152-1600 x-384 x^2\right ) \log (5)\right ) \log ^2(x)+(2 x+2 \log (5)) \log ^3(x)}{\log ^3(x)} \, dx=\left (x+\log (5)-\frac {16 x \left (x+(6+2 x)^2\right )}{\log (x)}\right )^2 \]
Time = 2.08 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.91 \[ \int \frac {-663552 x-921600 x^2-467456 x^3-102400 x^4-8192 x^5+\left (664704 x+1383200 x^2+935040 x^3+256000 x^4+24576 x^5+\left (1152+800 x+128 x^2\right ) \log (5)\right ) \log (x)+\left (-2304 x-2400 x^2-512 x^3+\left (-1152-1600 x-384 x^2\right ) \log (5)\right ) \log ^2(x)+(2 x+2 \log (5)) \log ^3(x)}{\log ^3(x)} \, dx=\frac {x \left (576+400 x+64 x^2-\log (x)\right ) \left (16 x \left (36+25 x+4 x^2\right )-(x+\log (25)) \log (x)\right )}{\log ^2(x)} \]
Integrate[(-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 - 16 00*x - 384*x^2)*Log[5])*Log[x]^2 + (2*x + 2*Log[5])*Log[x]^3)/Log[x]^3,x]
(x*(576 + 400*x + 64*x^2 - Log[x])*(16*x*(36 + 25*x + 4*x^2) - (x + Log[25 ])*Log[x]))/Log[x]^2
Result contains higher order function than in optimal. Order 4 vs. order 3 in optimal.
Time = 1.13 (sec) , antiderivative size = 186, normalized size of antiderivative = 8.45, number of steps used = 5, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.044, Rules used = {7239, 27, 25, 7293, 2009}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {-8192 x^5-102400 x^4-467456 x^3-921600 x^2+\left (-512 x^3-2400 x^2+\left (-384 x^2-1600 x-1152\right ) \log (5)-2304 x\right ) \log ^2(x)+\left (24576 x^5+256000 x^4+935040 x^3+1383200 x^2+\left (128 x^2+800 x+1152\right ) \log (5)+664704 x\right ) \log (x)-663552 x+(2 x+2 \log (5)) \log ^3(x)}{\log ^3(x)} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 \left (16 x \left (4 x^2+25 x+36\right )-(x+\log (5)) \log (x)\right ) \left (-16 \left (4 x^2+25 x+36\right )+32 \left (6 x^2+25 x+18\right ) \log (x)-\log ^2(x)\right )}{\log ^3(x)}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int -\frac {\left (16 x \left (4 x^2+25 x+36\right )-(x+\log (5)) \log (x)\right ) \left (\log ^2(x)-32 \left (6 x^2+25 x+18\right ) \log (x)+16 \left (4 x^2+25 x+36\right )\right )}{\log ^3(x)}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -2 \int \frac {\left (16 x \left (4 x^2+25 x+36\right )-(x+\log (5)) \log (x)\right ) \left (\log ^2(x)-32 \left (6 x^2+25 x+18\right ) \log (x)+16 \left (4 x^2+25 x+36\right )\right )}{\log ^3(x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {256 x (x+4)^2 (4 x+9)^2}{\log ^3(x)}-x+\frac {16 \left (16 x^3+3 (25+\log (625)) x^2+2 (36+25 \log (5)) x+36 \log (5)\right )}{\log (x)}-\frac {16 \left (4 x^2+25 x+36\right ) \left (192 x^3+800 x^2+577 x+\log (5)\right )}{\log ^2(x)}-\log (5)\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -2 \left (663552 \operatorname {ExpIntegralEi}(2 \log (x))+2073600 \operatorname {ExpIntegralEi}(3 \log (x))-48 (43225+\log (625)) \operatorname {ExpIntegralEi}(3 \log (x))+48 (25+\log (625)) \operatorname {ExpIntegralEi}(3 \log (x))-32 (20772+25 \log (5)) \operatorname {ExpIntegralEi}(2 \log (x))+32 (36+25 \log (5)) \operatorname {ExpIntegralEi}(2 \log (x))-\frac {2048 x^6}{\log ^2(x)}-\frac {25600 x^5}{\log ^2(x)}-\frac {116864 x^4}{\log ^2(x)}+\frac {64 x^4}{\log (x)}-\frac {230400 x^3}{\log ^2(x)}+\frac {16 x^3 (43225+\log (625))}{\log (x)}-\frac {691200 x^3}{\log (x)}-\frac {x^2}{2}-\frac {165888 x^2}{\log ^2(x)}+\frac {16 x^2 (20772+25 \log (5))}{\log (x)}-\frac {331776 x^2}{\log (x)}+\frac {576 x \log (5)}{\log (x)}-x \log (5)\right )\) |
Int[(-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 + 1 28*x^2)*Log[5])*Log[x] + (-2304*x - 2400*x^2 - 512*x^3 + (-1152 - 1600*x - 384*x^2)*Log[5])*Log[x]^2 + (2*x + 2*Log[5])*Log[x]^3)/Log[x]^3,x]
-2*(-1/2*x^2 + 663552*ExpIntegralEi[2*Log[x]] + 2073600*ExpIntegralEi[3*Lo g[x]] - x*Log[5] + 32*ExpIntegralEi[2*Log[x]]*(36 + 25*Log[5]) - 32*ExpInt egralEi[2*Log[x]]*(20772 + 25*Log[5]) + 48*ExpIntegralEi[3*Log[x]]*(25 + L og[625]) - 48*ExpIntegralEi[3*Log[x]]*(43225 + Log[625]) - (165888*x^2)/Lo g[x]^2 - (230400*x^3)/Log[x]^2 - (116864*x^4)/Log[x]^2 - (25600*x^5)/Log[x ]^2 - (2048*x^6)/Log[x]^2 - (331776*x^2)/Log[x] - (691200*x^3)/Log[x] + (6 4*x^4)/Log[x] + (576*x*Log[5])/Log[x] + (16*x^2*(20772 + 25*Log[5]))/Log[x ] + (16*x^3*(43225 + Log[625]))/Log[x])
3.3.7.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
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 | \(\frac {331776 x^{2}}{\ln \left (x \right )^{2}}-\frac {128 x^{4}}{\ln \left (x \right )}+2 x \ln \left (5\right )+1152 \ln \left (5\right ) \left (-\frac {x}{\ln \left (x \right )}-\operatorname {Ei}_{1}\left (-\ln \left (x \right )\right )\right )+800 \ln \left (5\right ) \left (-\frac {x^{2}}{\ln \left (x \right )}-2 \,\operatorname {Ei}_{1}\left (-2 \ln \left (x \right )\right )\right )+128 \ln \left (5\right ) \left (-\frac {x^{3}}{\ln \left (x \right )}-3 \,\operatorname {Ei}_{1}\left (-3 \ln \left (x \right )\right )\right )+1152 \ln \left (5\right ) \operatorname {Ei}_{1}\left (-\ln \left (x \right )\right )+\frac {4096 x^{6}}{\ln \left (x \right )^{2}}+1600 \ln \left (5\right ) \operatorname {Ei}_{1}\left (-2 \ln \left (x \right )\right )+384 \ln \left (5\right ) \operatorname {Ei}_{1}\left (-3 \ln \left (x \right )\right )+\frac {51200 x^{5}}{\ln \left (x \right )^{2}}-\frac {800 x^{3}}{\ln \left (x \right )}+\frac {233728 x^{4}}{\ln \left (x \right )^{2}}+\frac {460800 x^{3}}{\ln \left (x \right )^{2}}-\frac {1152 x^{2}}{\ln \left (x \right )}+x^{2}\) | \(176\) |
int(((2*ln(5)+2*x)*ln(x)^3+((-384*x^2-1600*x-1152)*ln(5)-512*x^3-2400*x^2- 2304*x)*ln(x)^2+((128*x^2+800*x+1152)*ln(5)+24576*x^5+256000*x^4+935040*x^ 3+1383200*x^2+664704*x)*ln(x)-8192*x^5-102400*x^4-467456*x^3-921600*x^2-66 3552*x)/ln(x)^3,x,method=_RETURNVERBOSE)
2*x*ln(5)+x^2-32*x*(-128*x^5+4*x^2*ln(5)*ln(x)-1600*x^4+4*x^3*ln(x)+25*x*l n(5)*ln(x)-7304*x^3+25*x^2*ln(x)+36*ln(5)*ln(x)-14400*x^2+36*x*ln(x)-10368 *x)/ln(x)^2
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 \[ \int \frac {-663552 x-921600 x^2-467456 x^3-102400 x^4-8192 x^5+\left (664704 x+1383200 x^2+935040 x^3+256000 x^4+24576 x^5+\left (1152+800 x+128 x^2\right ) \log (5)\right ) \log (x)+\left (-2304 x-2400 x^2-512 x^3+\left (-1152-1600 x-384 x^2\right ) \log (5)\right ) \log ^2(x)+(2 x+2 \log (5)) \log ^3(x)}{\log ^3(x)} \, dx=\frac {4096 \, x^{6} + 51200 \, x^{5} + 233728 \, x^{4} + 460800 \, x^{3} + {\left (x^{2} + 2 \, x \log \left (5\right )\right )} \log \left (x\right )^{2} + 331776 \, x^{2} - 32 \, {\left (4 \, x^{4} + 25 \, x^{3} + 36 \, x^{2} + {\left (4 \, x^{3} + 25 \, x^{2} + 36 \, x\right )} \log \left (5\right )\right )} \log \left (x\right )}{\log \left (x\right )^{2}} \]
integrate(((2*log(5)+2*x)*log(x)^3+((-384*x^2-1600*x-1152)*log(5)-512*x^3- 2400*x^2-2304*x)*log(x)^2+((128*x^2+800*x+1152)*log(5)+24576*x^5+256000*x^ 4+935040*x^3+1383200*x^2+664704*x)*log(x)-8192*x^5-102400*x^4-467456*x^3-9 21600*x^2-663552*x)/log(x)^3,x, algorithm=\
(4096*x^6 + 51200*x^5 + 233728*x^4 + 460800*x^3 + (x^2 + 2*x*log(5))*log(x )^2 + 331776*x^2 - 32*(4*x^4 + 25*x^3 + 36*x^2 + (4*x^3 + 25*x^2 + 36*x)*l og(5))*log(x))/log(x)^2
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 \[ \int \frac {-663552 x-921600 x^2-467456 x^3-102400 x^4-8192 x^5+\left (664704 x+1383200 x^2+935040 x^3+256000 x^4+24576 x^5+\left (1152+800 x+128 x^2\right ) \log (5)\right ) \log (x)+\left (-2304 x-2400 x^2-512 x^3+\left (-1152-1600 x-384 x^2\right ) \log (5)\right ) \log ^2(x)+(2 x+2 \log (5)) \log ^3(x)}{\log ^3(x)} \, dx=x^{2} + 2 x \log {\left (5 \right )} + \frac {4096 x^{6} + 51200 x^{5} + 233728 x^{4} + 460800 x^{3} + 331776 x^{2} + \left (- 128 x^{4} - 800 x^{3} - 128 x^{3} \log {\left (5 \right )} - 800 x^{2} \log {\left (5 \right )} - 1152 x^{2} - 1152 x \log {\left (5 \right )}\right ) \log {\left (x \right )}}{\log {\left (x \right )}^{2}} \]
integrate(((2*ln(5)+2*x)*ln(x)**3+((-384*x**2-1600*x-1152)*ln(5)-512*x**3- 2400*x**2-2304*x)*ln(x)**2+((128*x**2+800*x+1152)*ln(5)+24576*x**5+256000* x**4+935040*x**3+1383200*x**2+664704*x)*ln(x)-8192*x**5-102400*x**4-467456 *x**3-921600*x**2-663552*x)/ln(x)**3,x)
x**2 + 2*x*log(5) + (4096*x**6 + 51200*x**5 + 233728*x**4 + 460800*x**3 + 331776*x**2 + (-128*x**4 - 800*x**3 - 128*x**3*log(5) - 800*x**2*log(5) - 1152*x**2 - 1152*x*log(5))*log(x))/log(x)**2
Result contains higher order function than in optimal. Order 4 vs. order 3.
Time = 0.25 (sec) , antiderivative size = 165, normalized size of antiderivative = 7.50 \[ \int \frac {-663552 x-921600 x^2-467456 x^3-102400 x^4-8192 x^5+\left (664704 x+1383200 x^2+935040 x^3+256000 x^4+24576 x^5+\left (1152+800 x+128 x^2\right ) \log (5)\right ) \log (x)+\left (-2304 x-2400 x^2-512 x^3+\left (-1152-1600 x-384 x^2\right ) \log (5)\right ) \log ^2(x)+(2 x+2 \log (5)) \log ^3(x)}{\log ^3(x)} \, dx=x^{2} + 2 \, x \log \left (5\right ) - 384 \, {\rm Ei}\left (3 \, \log \left (x\right )\right ) \log \left (5\right ) - 1600 \, {\rm Ei}\left (2 \, \log \left (x\right )\right ) \log \left (5\right ) - 1152 \, {\rm Ei}\left (\log \left (x\right )\right ) \log \left (5\right ) + 1152 \, \Gamma \left (-1, -\log \left (x\right )\right ) \log \left (5\right ) + 1600 \, \Gamma \left (-1, -2 \, \log \left (x\right )\right ) \log \left (5\right ) + 384 \, \Gamma \left (-1, -3 \, \log \left (x\right )\right ) \log \left (5\right ) - 512 \, {\rm Ei}\left (4 \, \log \left (x\right )\right ) - 2400 \, {\rm Ei}\left (3 \, \log \left (x\right )\right ) - 2304 \, {\rm Ei}\left (2 \, \log \left (x\right )\right ) + 1329408 \, \Gamma \left (-1, -2 \, \log \left (x\right )\right ) + 4149600 \, \Gamma \left (-1, -3 \, \log \left (x\right )\right ) + 3740160 \, \Gamma \left (-1, -4 \, \log \left (x\right )\right ) + 1280000 \, \Gamma \left (-1, -5 \, \log \left (x\right )\right ) + 147456 \, \Gamma \left (-1, -6 \, \log \left (x\right )\right ) + 2654208 \, \Gamma \left (-2, -2 \, \log \left (x\right )\right ) + 8294400 \, \Gamma \left (-2, -3 \, \log \left (x\right )\right ) + 7479296 \, \Gamma \left (-2, -4 \, \log \left (x\right )\right ) + 2560000 \, \Gamma \left (-2, -5 \, \log \left (x\right )\right ) + 294912 \, \Gamma \left (-2, -6 \, \log \left (x\right )\right ) \]
integrate(((2*log(5)+2*x)*log(x)^3+((-384*x^2-1600*x-1152)*log(5)-512*x^3- 2400*x^2-2304*x)*log(x)^2+((128*x^2+800*x+1152)*log(5)+24576*x^5+256000*x^ 4+935040*x^3+1383200*x^2+664704*x)*log(x)-8192*x^5-102400*x^4-467456*x^3-9 21600*x^2-663552*x)/log(x)^3,x, algorithm=\
x^2 + 2*x*log(5) - 384*Ei(3*log(x))*log(5) - 1600*Ei(2*log(x))*log(5) - 11 52*Ei(log(x))*log(5) + 1152*gamma(-1, -log(x))*log(5) + 1600*gamma(-1, -2* log(x))*log(5) + 384*gamma(-1, -3*log(x))*log(5) - 512*Ei(4*log(x)) - 2400 *Ei(3*log(x)) - 2304*Ei(2*log(x)) + 1329408*gamma(-1, -2*log(x)) + 4149600 *gamma(-1, -3*log(x)) + 3740160*gamma(-1, -4*log(x)) + 1280000*gamma(-1, - 5*log(x)) + 147456*gamma(-1, -6*log(x)) + 2654208*gamma(-2, -2*log(x)) + 8 294400*gamma(-2, -3*log(x)) + 7479296*gamma(-2, -4*log(x)) + 2560000*gamma (-2, -5*log(x)) + 294912*gamma(-2, -6*log(x))
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 \[ \int \frac {-663552 x-921600 x^2-467456 x^3-102400 x^4-8192 x^5+\left (664704 x+1383200 x^2+935040 x^3+256000 x^4+24576 x^5+\left (1152+800 x+128 x^2\right ) \log (5)\right ) \log (x)+\left (-2304 x-2400 x^2-512 x^3+\left (-1152-1600 x-384 x^2\right ) \log (5)\right ) \log ^2(x)+(2 x+2 \log (5)) \log ^3(x)}{\log ^3(x)} \, dx=\frac {4096 \, x^{6}}{\log \left (x\right )^{2}} + \frac {51200 \, x^{5}}{\log \left (x\right )^{2}} - \frac {128 \, x^{4}}{\log \left (x\right )} - \frac {128 \, x^{3} \log \left (5\right )}{\log \left (x\right )} + x^{2} + 2 \, x \log \left (5\right ) + \frac {233728 \, x^{4}}{\log \left (x\right )^{2}} - \frac {800 \, x^{3}}{\log \left (x\right )} - \frac {800 \, x^{2} \log \left (5\right )}{\log \left (x\right )} + \frac {460800 \, x^{3}}{\log \left (x\right )^{2}} - \frac {1152 \, x^{2}}{\log \left (x\right )} - \frac {1152 \, x \log \left (5\right )}{\log \left (x\right )} + \frac {331776 \, x^{2}}{\log \left (x\right )^{2}} \]
integrate(((2*log(5)+2*x)*log(x)^3+((-384*x^2-1600*x-1152)*log(5)-512*x^3- 2400*x^2-2304*x)*log(x)^2+((128*x^2+800*x+1152)*log(5)+24576*x^5+256000*x^ 4+935040*x^3+1383200*x^2+664704*x)*log(x)-8192*x^5-102400*x^4-467456*x^3-9 21600*x^2-663552*x)/log(x)^3,x, algorithm=\
4096*x^6/log(x)^2 + 51200*x^5/log(x)^2 - 128*x^4/log(x) - 128*x^3*log(5)/l og(x) + x^2 + 2*x*log(5) + 233728*x^4/log(x)^2 - 800*x^3/log(x) - 800*x^2* log(5)/log(x) + 460800*x^3/log(x)^2 - 1152*x^2/log(x) - 1152*x*log(5)/log( x) + 331776*x^2/log(x)^2
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(-(663552*x + log(x)^2*(2304*x + log(5)*(1600*x + 384*x^2 + 1152) + 240 0*x^2 + 512*x^3) - log(x)*(664704*x + log(5)*(800*x + 128*x^2 + 1152) + 13 83200*x^2 + 935040*x^3 + 256000*x^4 + 24576*x^5) - log(x)^3*(2*x + 2*log(5 )) + 921600*x^2 + 467456*x^3 + 102400*x^4 + 8192*x^5)/log(x)^3,x)