\(\int \frac {128 x^{14}+64 x^{15}+8 x^{16}+(64 x^{14}+288 x^{15}+140 x^{16}+18 x^{17}) \log (3 x)+(384 x^{13}+192 x^{14}+24 x^{15}+(192 x^{13}+1056 x^{14}+524 x^{15}+68 x^{16}) \log (3 x)) \log (x \log ^2(3 x))+(384 x^{12}+192 x^{13}+24 x^{14}+(192 x^{12}+1440 x^{13}+732 x^{14}+96 x^{15}) \log (3 x)) \log ^2(x \log ^2(3 x))+(128 x^{11}+64 x^{12}+8 x^{13}+(64 x^{11}+864 x^{12}+452 x^{13}+60 x^{14}) \log (3 x)) \log ^3(x \log ^2(3 x))+(192 x^{11}+104 x^{12}+14 x^{13}) \log (3 x) \log ^4(x \log ^2(3 x))}{\log (3 x)} \, dx\) [9342]

Optimal result

Integrand size = 241, antiderivative size = 22 \[ \int \frac {128 x^{14}+64 x^{15}+8 x^{16}+\left (64 x^{14}+288 x^{15}+140 x^{16}+18 x^{17}\right ) \log (3 x)+\left (384 x^{13}+192 x^{14}+24 x^{15}+\left (192 x^{13}+1056 x^{14}+524 x^{15}+68 x^{16}\right ) \log (3 x)\right ) \log \left (x \log ^2(3 x)\right )+\left (384 x^{12}+192 x^{13}+24 x^{14}+\left (192 x^{12}+1440 x^{13}+732 x^{14}+96 x^{15}\right ) \log (3 x)\right ) \log ^2\left (x \log ^2(3 x)\right )+\left (128 x^{11}+64 x^{12}+8 x^{13}+\left (64 x^{11}+864 x^{12}+452 x^{13}+60 x^{14}\right ) \log (3 x)\right ) \log ^3\left (x \log ^2(3 x)\right )+\left (192 x^{11}+104 x^{12}+14 x^{13}\right ) \log (3 x) \log ^4\left (x \log ^2(3 x)\right )}{\log (3 x)} \, dx=x^{12} (4+x)^2 \left (x+\log \left (x \log ^2(3 x)\right )\right )^4 \]

[Out]

(4+x)^2*x^12*(ln(x*ln(3*x)^2)+x)^4

Rubi [F]

\[ \int \frac {128 x^{14}+64 x^{15}+8 x^{16}+\left (64 x^{14}+288 x^{15}+140 x^{16}+18 x^{17}\right ) \log (3 x)+\left (384 x^{13}+192 x^{14}+24 x^{15}+\left (192 x^{13}+1056 x^{14}+524 x^{15}+68 x^{16}\right ) \log (3 x)\right ) \log \left (x \log ^2(3 x)\right )+\left (384 x^{12}+192 x^{13}+24 x^{14}+\left (192 x^{12}+1440 x^{13}+732 x^{14}+96 x^{15}\right ) \log (3 x)\right ) \log ^2\left (x \log ^2(3 x)\right )+\left (128 x^{11}+64 x^{12}+8 x^{13}+\left (64 x^{11}+864 x^{12}+452 x^{13}+60 x^{14}\right ) \log (3 x)\right ) \log ^3\left (x \log ^2(3 x)\right )+\left (192 x^{11}+104 x^{12}+14 x^{13}\right ) \log (3 x) \log ^4\left (x \log ^2(3 x)\right )}{\log (3 x)} \, dx=\int \frac {128 x^{14}+64 x^{15}+8 x^{16}+\left (64 x^{14}+288 x^{15}+140 x^{16}+18 x^{17}\right ) \log (3 x)+\left (384 x^{13}+192 x^{14}+24 x^{15}+\left (192 x^{13}+1056 x^{14}+524 x^{15}+68 x^{16}\right ) \log (3 x)\right ) \log \left (x \log ^2(3 x)\right )+\left (384 x^{12}+192 x^{13}+24 x^{14}+\left (192 x^{12}+1440 x^{13}+732 x^{14}+96 x^{15}\right ) \log (3 x)\right ) \log ^2\left (x \log ^2(3 x)\right )+\left (128 x^{11}+64 x^{12}+8 x^{13}+\left (64 x^{11}+864 x^{12}+452 x^{13}+60 x^{14}\right ) \log (3 x)\right ) \log ^3\left (x \log ^2(3 x)\right )+\left (192 x^{11}+104 x^{12}+14 x^{13}\right ) \log (3 x) \log ^4\left (x \log ^2(3 x)\right )}{\log (3 x)} \, dx \]

[In]

Int[(128*x^14 + 64*x^15 + 8*x^16 + (64*x^14 + 288*x^15 + 140*x^16 + 18*x^17)*Log[3*x] + (384*x^13 + 192*x^14 +
24*x^15 + (192*x^13 + 1056*x^14 + 524*x^15 + 68*x^16)*Log[3*x])*Log[x*Log[3*x]^2] + (384*x^12 + 192*x^13 + 24
*x^14 + (192*x^12 + 1440*x^13 + 732*x^14 + 96*x^15)*Log[3*x])*Log[x*Log[3*x]^2]^2 + (128*x^11 + 64*x^12 + 8*x^
13 + (64*x^11 + 864*x^12 + 452*x^13 + 60*x^14)*Log[3*x])*Log[x*Log[3*x]^2]^3 + (192*x^11 + 104*x^12 + 14*x^13)
*Log[3*x]*Log[x*Log[3*x]^2]^4)/Log[3*x],x]

[Out]

(-48*x^14)/49 - (32*x^15)/75 + (1021*x^16)/64 + 8*x^17 + x^18 + (128*ExpIntegralEi[15*Log[3*x]])/14348907 + (6
4*ExpIntegralEi[16*Log[3*x]])/43046721 + (8*ExpIntegralEi[17*Log[3*x]])/129140163 + (32*ExpIntegralEi[14*Log[3
*x]]*Log[3*x])/11160261 + (352*ExpIntegralEi[15*Log[3*x]]*Log[3*x])/71744535 + (131*ExpIntegralEi[16*Log[3*x]]
*Log[3*x])/172186884 + (4*ExpIntegralEi[17*Log[3*x]]*Log[3*x])/129140163 - (32*ExpIntegralEi[14*Log[3*x]]*(2 +
Log[3*x]))/11160261 - (352*ExpIntegralEi[15*Log[3*x]]*(2 + Log[3*x]))/71744535 - (131*ExpIntegralEi[16*Log[3*
x]]*(2 + Log[3*x]))/172186884 - (4*ExpIntegralEi[17*Log[3*x]]*(2 + Log[3*x]))/129140163 + (96*x^14*Log[x*Log[3
*x]^2])/7 + (352*x^15*Log[x*Log[3*x]^2])/5 + (131*x^16*Log[x*Log[3*x]^2])/4 + 4*x^17*Log[x*Log[3*x]^2] + 384*D
efer[Int][(x^13*Log[x*Log[3*x]^2])/Log[3*x], x] + 192*Defer[Int][(x^14*Log[x*Log[3*x]^2])/Log[3*x], x] + 24*De
fer[Int][(x^15*Log[x*Log[3*x]^2])/Log[3*x], x] + 192*Defer[Int][x^12*Log[x*Log[3*x]^2]^2, x] + 1440*Defer[Int]
[x^13*Log[x*Log[3*x]^2]^2, x] + 732*Defer[Int][x^14*Log[x*Log[3*x]^2]^2, x] + 96*Defer[Int][x^15*Log[x*Log[3*x
]^2]^2, x] + 384*Defer[Int][(x^12*Log[x*Log[3*x]^2]^2)/Log[3*x], x] + 192*Defer[Int][(x^13*Log[x*Log[3*x]^2]^2
)/Log[3*x], x] + 24*Defer[Int][(x^14*Log[x*Log[3*x]^2]^2)/Log[3*x], x] + 64*Defer[Int][x^11*Log[x*Log[3*x]^2]^
3, x] + 864*Defer[Int][x^12*Log[x*Log[3*x]^2]^3, x] + 452*Defer[Int][x^13*Log[x*Log[3*x]^2]^3, x] + 60*Defer[I
nt][x^14*Log[x*Log[3*x]^2]^3, x] + 128*Defer[Int][(x^11*Log[x*Log[3*x]^2]^3)/Log[3*x], x] + 64*Defer[Int][(x^1
2*Log[x*Log[3*x]^2]^3)/Log[3*x], x] + 8*Defer[Int][(x^13*Log[x*Log[3*x]^2]^3)/Log[3*x], x] + 192*Defer[Int][x^
11*Log[x*Log[3*x]^2]^4, x] + 104*Defer[Int][x^12*Log[x*Log[3*x]^2]^4, x] + 14*Defer[Int][x^13*Log[x*Log[3*x]^2
]^4, x]

Rubi steps Aborted

Mathematica [A] (verified)

Time = 5.09 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \frac {128 x^{14}+64 x^{15}+8 x^{16}+\left (64 x^{14}+288 x^{15}+140 x^{16}+18 x^{17}\right ) \log (3 x)+\left (384 x^{13}+192 x^{14}+24 x^{15}+\left (192 x^{13}+1056 x^{14}+524 x^{15}+68 x^{16}\right ) \log (3 x)\right ) \log \left (x \log ^2(3 x)\right )+\left (384 x^{12}+192 x^{13}+24 x^{14}+\left (192 x^{12}+1440 x^{13}+732 x^{14}+96 x^{15}\right ) \log (3 x)\right ) \log ^2\left (x \log ^2(3 x)\right )+\left (128 x^{11}+64 x^{12}+8 x^{13}+\left (64 x^{11}+864 x^{12}+452 x^{13}+60 x^{14}\right ) \log (3 x)\right ) \log ^3\left (x \log ^2(3 x)\right )+\left (192 x^{11}+104 x^{12}+14 x^{13}\right ) \log (3 x) \log ^4\left (x \log ^2(3 x)\right )}{\log (3 x)} \, dx=x^{12} (4+x)^2 \left (x+\log \left (x \log ^2(3 x)\right )\right )^4 \]

[In]

Integrate[(128*x^14 + 64*x^15 + 8*x^16 + (64*x^14 + 288*x^15 + 140*x^16 + 18*x^17)*Log[3*x] + (384*x^13 + 192*
x^14 + 24*x^15 + (192*x^13 + 1056*x^14 + 524*x^15 + 68*x^16)*Log[3*x])*Log[x*Log[3*x]^2] + (384*x^12 + 192*x^1
3 + 24*x^14 + (192*x^12 + 1440*x^13 + 732*x^14 + 96*x^15)*Log[3*x])*Log[x*Log[3*x]^2]^2 + (128*x^11 + 64*x^12
+ 8*x^13 + (64*x^11 + 864*x^12 + 452*x^13 + 60*x^14)*Log[3*x])*Log[x*Log[3*x]^2]^3 + (192*x^11 + 104*x^12 + 14
*x^13)*Log[3*x]*Log[x*Log[3*x]^2]^4)/Log[3*x],x]

[Out]

x^12*(4 + x)^2*(x + Log[x*Log[3*x]^2])^4

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(199\) vs. \(2(22)=44\).

Time = 8.10 (sec) , antiderivative size = 200, normalized size of antiderivative = 9.09

method	result	size
parallelrisch	\(x^{18}+4 \ln \left (x \ln \left (3 x \right )^{2}\right ) x^{17}+6 \ln \left (x \ln \left (3 x \right )^{2}\right )^{2} x^{16}+4 \ln \left (x \ln \left (3 x \right )^{2}\right )^{3} x^{15}+x^{14} \ln \left (x \ln \left (3 x \right )^{2}\right )^{4}+8 x^{17}+32 \ln \left (x \ln \left (3 x \right )^{2}\right ) x^{16}+48 \ln \left (x \ln \left (3 x \right )^{2}\right )^{2} x^{15}+32 \ln \left (x \ln \left (3 x \right )^{2}\right )^{3} x^{14}+8 \ln \left (x \ln \left (3 x \right )^{2}\right )^{4} x^{13}+16 x^{16}+64 \ln \left (x \ln \left (3 x \right )^{2}\right ) x^{15}+96 \ln \left (x \ln \left (3 x \right )^{2}\right )^{2} x^{14}+64 \ln \left (x \ln \left (3 x \right )^{2}\right )^{3} x^{13}+16 \ln \left (x \ln \left (3 x \right )^{2}\right )^{4} x^{12}\)	\(200\)

[In]

int(((14*x^13+104*x^12+192*x^11)*ln(3*x)*ln(x*ln(3*x)^2)^4+((60*x^14+452*x^13+864*x^12+64*x^11)*ln(3*x)+8*x^13
+64*x^12+128*x^11)*ln(x*ln(3*x)^2)^3+((96*x^15+732*x^14+1440*x^13+192*x^12)*ln(3*x)+24*x^14+192*x^13+384*x^12)
*ln(x*ln(3*x)^2)^2+((68*x^16+524*x^15+1056*x^14+192*x^13)*ln(3*x)+24*x^15+192*x^14+384*x^13)*ln(x*ln(3*x)^2)+(
18*x^17+140*x^16+288*x^15+64*x^14)*ln(3*x)+8*x^16+64*x^15+128*x^14)/ln(3*x),x,method=_RETURNVERBOSE)

[Out]

x^18+4*ln(x*ln(3*x)^2)*x^17+6*ln(x*ln(3*x)^2)^2*x^16+4*ln(x*ln(3*x)^2)^3*x^15+x^14*ln(x*ln(3*x)^2)^4+8*x^17+32
*ln(x*ln(3*x)^2)*x^16+48*ln(x*ln(3*x)^2)^2*x^15+32*ln(x*ln(3*x)^2)^3*x^14+8*ln(x*ln(3*x)^2)^4*x^13+16*x^16+64*
ln(x*ln(3*x)^2)*x^15+96*ln(x*ln(3*x)^2)^2*x^14+64*ln(x*ln(3*x)^2)^3*x^13+16*ln(x*ln(3*x)^2)^4*x^12

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 119 vs. \(2 (22) = 44\).

Time = 0.27 (sec) , antiderivative size = 119, normalized size of antiderivative = 5.41 \[ \int \frac {128 x^{14}+64 x^{15}+8 x^{16}+\left (64 x^{14}+288 x^{15}+140 x^{16}+18 x^{17}\right ) \log (3 x)+\left (384 x^{13}+192 x^{14}+24 x^{15}+\left (192 x^{13}+1056 x^{14}+524 x^{15}+68 x^{16}\right ) \log (3 x)\right ) \log \left (x \log ^2(3 x)\right )+\left (384 x^{12}+192 x^{13}+24 x^{14}+\left (192 x^{12}+1440 x^{13}+732 x^{14}+96 x^{15}\right ) \log (3 x)\right ) \log ^2\left (x \log ^2(3 x)\right )+\left (128 x^{11}+64 x^{12}+8 x^{13}+\left (64 x^{11}+864 x^{12}+452 x^{13}+60 x^{14}\right ) \log (3 x)\right ) \log ^3\left (x \log ^2(3 x)\right )+\left (192 x^{11}+104 x^{12}+14 x^{13}\right ) \log (3 x) \log ^4\left (x \log ^2(3 x)\right )}{\log (3 x)} \, dx=x^{18} + 8 \, x^{17} + 16 \, x^{16} + {\left (x^{14} + 8 \, x^{13} + 16 \, x^{12}\right )} \log \left (x \log \left (3 \, x\right )^{2}\right )^{4} + 4 \, {\left (x^{15} + 8 \, x^{14} + 16 \, x^{13}\right )} \log \left (x \log \left (3 \, x\right )^{2}\right )^{3} + 6 \, {\left (x^{16} + 8 \, x^{15} + 16 \, x^{14}\right )} \log \left (x \log \left (3 \, x\right )^{2}\right )^{2} + 4 \, {\left (x^{17} + 8 \, x^{16} + 16 \, x^{15}\right )} \log \left (x \log \left (3 \, x\right )^{2}\right ) \]

[In]

integrate(((14*x^13+104*x^12+192*x^11)*log(3*x)*log(x*log(3*x)^2)^4+((60*x^14+452*x^13+864*x^12+64*x^11)*log(3
*x)+8*x^13+64*x^12+128*x^11)*log(x*log(3*x)^2)^3+((96*x^15+732*x^14+1440*x^13+192*x^12)*log(3*x)+24*x^14+192*x
^13+384*x^12)*log(x*log(3*x)^2)^2+((68*x^16+524*x^15+1056*x^14+192*x^13)*log(3*x)+24*x^15+192*x^14+384*x^13)*l
og(x*log(3*x)^2)+(18*x^17+140*x^16+288*x^15+64*x^14)*log(3*x)+8*x^16+64*x^15+128*x^14)/log(3*x),x, algorithm="
fricas")

[Out]

x^18 + 8*x^17 + 16*x^16 + (x^14 + 8*x^13 + 16*x^12)*log(x*log(3*x)^2)^4 + 4*(x^15 + 8*x^14 + 16*x^13)*log(x*lo
g(3*x)^2)^3 + 6*(x^16 + 8*x^15 + 16*x^14)*log(x*log(3*x)^2)^2 + 4*(x^17 + 8*x^16 + 16*x^15)*log(x*log(3*x)^2)

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 117 vs. \(2 (20) = 40\).

Time = 0.43 (sec) , antiderivative size = 117, normalized size of antiderivative = 5.32 \[ \int \frac {128 x^{14}+64 x^{15}+8 x^{16}+\left (64 x^{14}+288 x^{15}+140 x^{16}+18 x^{17}\right ) \log (3 x)+\left (384 x^{13}+192 x^{14}+24 x^{15}+\left (192 x^{13}+1056 x^{14}+524 x^{15}+68 x^{16}\right ) \log (3 x)\right ) \log \left (x \log ^2(3 x)\right )+\left (384 x^{12}+192 x^{13}+24 x^{14}+\left (192 x^{12}+1440 x^{13}+732 x^{14}+96 x^{15}\right ) \log (3 x)\right ) \log ^2\left (x \log ^2(3 x)\right )+\left (128 x^{11}+64 x^{12}+8 x^{13}+\left (64 x^{11}+864 x^{12}+452 x^{13}+60 x^{14}\right ) \log (3 x)\right ) \log ^3\left (x \log ^2(3 x)\right )+\left (192 x^{11}+104 x^{12}+14 x^{13}\right ) \log (3 x) \log ^4\left (x \log ^2(3 x)\right )}{\log (3 x)} \, dx=x^{18} + 8 x^{17} + 16 x^{16} + \left (x^{14} + 8 x^{13} + 16 x^{12}\right ) \log {\left (x \log {\left (3 x \right )}^{2} \right )}^{4} + \left (4 x^{15} + 32 x^{14} + 64 x^{13}\right ) \log {\left (x \log {\left (3 x \right )}^{2} \right )}^{3} + \left (6 x^{16} + 48 x^{15} + 96 x^{14}\right ) \log {\left (x \log {\left (3 x \right )}^{2} \right )}^{2} + \left (4 x^{17} + 32 x^{16} + 64 x^{15}\right ) \log {\left (x \log {\left (3 x \right )}^{2} \right )} \]

[In]

integrate(((14*x**13+104*x**12+192*x**11)*ln(3*x)*ln(x*ln(3*x)**2)**4+((60*x**14+452*x**13+864*x**12+64*x**11)
*ln(3*x)+8*x**13+64*x**12+128*x**11)*ln(x*ln(3*x)**2)**3+((96*x**15+732*x**14+1440*x**13+192*x**12)*ln(3*x)+24
*x**14+192*x**13+384*x**12)*ln(x*ln(3*x)**2)**2+((68*x**16+524*x**15+1056*x**14+192*x**13)*ln(3*x)+24*x**15+19
2*x**14+384*x**13)*ln(x*ln(3*x)**2)+(18*x**17+140*x**16+288*x**15+64*x**14)*ln(3*x)+8*x**16+64*x**15+128*x**14
)/ln(3*x),x)

[Out]

x**18 + 8*x**17 + 16*x**16 + (x**14 + 8*x**13 + 16*x**12)*log(x*log(3*x)**2)**4 + (4*x**15 + 32*x**14 + 64*x**
13)*log(x*log(3*x)**2)**3 + (6*x**16 + 48*x**15 + 96*x**14)*log(x*log(3*x)**2)**2 + (4*x**17 + 32*x**16 + 64*x
**15)*log(x*log(3*x)**2)

Maxima [F]

\[ \int \frac {128 x^{14}+64 x^{15}+8 x^{16}+\left (64 x^{14}+288 x^{15}+140 x^{16}+18 x^{17}\right ) \log (3 x)+\left (384 x^{13}+192 x^{14}+24 x^{15}+\left (192 x^{13}+1056 x^{14}+524 x^{15}+68 x^{16}\right ) \log (3 x)\right ) \log \left (x \log ^2(3 x)\right )+\left (384 x^{12}+192 x^{13}+24 x^{14}+\left (192 x^{12}+1440 x^{13}+732 x^{14}+96 x^{15}\right ) \log (3 x)\right ) \log ^2\left (x \log ^2(3 x)\right )+\left (128 x^{11}+64 x^{12}+8 x^{13}+\left (64 x^{11}+864 x^{12}+452 x^{13}+60 x^{14}\right ) \log (3 x)\right ) \log ^3\left (x \log ^2(3 x)\right )+\left (192 x^{11}+104 x^{12}+14 x^{13}\right ) \log (3 x) \log ^4\left (x \log ^2(3 x)\right )}{\log (3 x)} \, dx=\int { \frac {2 \, {\left (4 \, x^{16} + 32 \, x^{15} + 64 \, x^{14} + {\left (7 \, x^{13} + 52 \, x^{12} + 96 \, x^{11}\right )} \log \left (x \log \left (3 \, x\right )^{2}\right )^{4} \log \left (3 \, x\right ) + 2 \, {\left (2 \, x^{13} + 16 \, x^{12} + 32 \, x^{11} + {\left (15 \, x^{14} + 113 \, x^{13} + 216 \, x^{12} + 16 \, x^{11}\right )} \log \left (3 \, x\right )\right )} \log \left (x \log \left (3 \, x\right )^{2}\right )^{3} + 6 \, {\left (2 \, x^{14} + 16 \, x^{13} + 32 \, x^{12} + {\left (8 \, x^{15} + 61 \, x^{14} + 120 \, x^{13} + 16 \, x^{12}\right )} \log \left (3 \, x\right )\right )} \log \left (x \log \left (3 \, x\right )^{2}\right )^{2} + 2 \, {\left (6 \, x^{15} + 48 \, x^{14} + 96 \, x^{13} + {\left (17 \, x^{16} + 131 \, x^{15} + 264 \, x^{14} + 48 \, x^{13}\right )} \log \left (3 \, x\right )\right )} \log \left (x \log \left (3 \, x\right )^{2}\right ) + {\left (9 \, x^{17} + 70 \, x^{16} + 144 \, x^{15} + 32 \, x^{14}\right )} \log \left (3 \, x\right )\right )}}{\log \left (3 \, x\right )} \,d x } \]

[In]

integrate(((14*x^13+104*x^12+192*x^11)*log(3*x)*log(x*log(3*x)^2)^4+((60*x^14+452*x^13+864*x^12+64*x^11)*log(3
*x)+8*x^13+64*x^12+128*x^11)*log(x*log(3*x)^2)^3+((96*x^15+732*x^14+1440*x^13+192*x^12)*log(3*x)+24*x^14+192*x
^13+384*x^12)*log(x*log(3*x)^2)^2+((68*x^16+524*x^15+1056*x^14+192*x^13)*log(3*x)+24*x^15+192*x^14+384*x^13)*l
og(x*log(3*x)^2)+(18*x^17+140*x^16+288*x^15+64*x^14)*log(3*x)+8*x^16+64*x^15+128*x^14)/log(3*x),x, algorithm="
maxima")

[Out]

x^18 + 8*x^17 + 16*x^16 + (x^14 + 8*x^13 + 16*x^12)*log(x)^4 + 16*(x^14 + 8*x^13 + 16*x^12)*log(log(3) + log(x
))^4 + 4*(x^15 + 8*x^14 + 16*x^13)*log(x)^3 + 32*(x^15 + 8*x^14 + 16*x^13 + (x^14 + 8*x^13 + 16*x^12)*log(x))*
log(log(3) + log(x))^3 + 6*(x^16 + 8*x^15 + 16*x^14)*log(x)^2 + 24*(x^16 + 8*x^15 + 16*x^14 + (x^14 + 8*x^13 +
16*x^12)*log(x)^2 + 2*(x^15 + 8*x^14 + 16*x^13)*log(x))*log(log(3) + log(x))^2 + 4*(x^17 + 8*x^16 + 16*x^15)*
log(x) + 8*(x^17 + 8*x^16 + 16*x^15 + (x^14 + 8*x^13 + 16*x^12)*log(x)^3 + 3*(x^15 + 8*x^14 + 16*x^13)*log(x)^
2 + 3*(x^16 + 8*x^15 + 16*x^14)*log(x))*log(log(3) + log(x)) + 8/129140163*Ei(17*log(3*x)) + 64/43046721*Ei(16
*log(3*x)) + 128/14348907*Ei(15*log(3*x)) - 2*integrate(4*(x^16 + 8*x^15 + 16*x^14)/(log(3) + log(x)), x)

Giac [F]

\[ \int \frac {128 x^{14}+64 x^{15}+8 x^{16}+\left (64 x^{14}+288 x^{15}+140 x^{16}+18 x^{17}\right ) \log (3 x)+\left (384 x^{13}+192 x^{14}+24 x^{15}+\left (192 x^{13}+1056 x^{14}+524 x^{15}+68 x^{16}\right ) \log (3 x)\right ) \log \left (x \log ^2(3 x)\right )+\left (384 x^{12}+192 x^{13}+24 x^{14}+\left (192 x^{12}+1440 x^{13}+732 x^{14}+96 x^{15}\right ) \log (3 x)\right ) \log ^2\left (x \log ^2(3 x)\right )+\left (128 x^{11}+64 x^{12}+8 x^{13}+\left (64 x^{11}+864 x^{12}+452 x^{13}+60 x^{14}\right ) \log (3 x)\right ) \log ^3\left (x \log ^2(3 x)\right )+\left (192 x^{11}+104 x^{12}+14 x^{13}\right ) \log (3 x) \log ^4\left (x \log ^2(3 x)\right )}{\log (3 x)} \, dx=\int { \frac {2 \, {\left (4 \, x^{16} + 32 \, x^{15} + 64 \, x^{14} + {\left (7 \, x^{13} + 52 \, x^{12} + 96 \, x^{11}\right )} \log \left (x \log \left (3 \, x\right )^{2}\right )^{4} \log \left (3 \, x\right ) + 2 \, {\left (2 \, x^{13} + 16 \, x^{12} + 32 \, x^{11} + {\left (15 \, x^{14} + 113 \, x^{13} + 216 \, x^{12} + 16 \, x^{11}\right )} \log \left (3 \, x\right )\right )} \log \left (x \log \left (3 \, x\right )^{2}\right )^{3} + 6 \, {\left (2 \, x^{14} + 16 \, x^{13} + 32 \, x^{12} + {\left (8 \, x^{15} + 61 \, x^{14} + 120 \, x^{13} + 16 \, x^{12}\right )} \log \left (3 \, x\right )\right )} \log \left (x \log \left (3 \, x\right )^{2}\right )^{2} + 2 \, {\left (6 \, x^{15} + 48 \, x^{14} + 96 \, x^{13} + {\left (17 \, x^{16} + 131 \, x^{15} + 264 \, x^{14} + 48 \, x^{13}\right )} \log \left (3 \, x\right )\right )} \log \left (x \log \left (3 \, x\right )^{2}\right ) + {\left (9 \, x^{17} + 70 \, x^{16} + 144 \, x^{15} + 32 \, x^{14}\right )} \log \left (3 \, x\right )\right )}}{\log \left (3 \, x\right )} \,d x } \]

[In]

integrate(((14*x^13+104*x^12+192*x^11)*log(3*x)*log(x*log(3*x)^2)^4+((60*x^14+452*x^13+864*x^12+64*x^11)*log(3
*x)+8*x^13+64*x^12+128*x^11)*log(x*log(3*x)^2)^3+((96*x^15+732*x^14+1440*x^13+192*x^12)*log(3*x)+24*x^14+192*x
^13+384*x^12)*log(x*log(3*x)^2)^2+((68*x^16+524*x^15+1056*x^14+192*x^13)*log(3*x)+24*x^15+192*x^14+384*x^13)*l
og(x*log(3*x)^2)+(18*x^17+140*x^16+288*x^15+64*x^14)*log(3*x)+8*x^16+64*x^15+128*x^14)/log(3*x),x, algorithm="
giac")

[Out]

integrate(2*(4*x^16 + 32*x^15 + 64*x^14 + (7*x^13 + 52*x^12 + 96*x^11)*log(x*log(3*x)^2)^4*log(3*x) + 2*(2*x^1
3 + 16*x^12 + 32*x^11 + (15*x^14 + 113*x^13 + 216*x^12 + 16*x^11)*log(3*x))*log(x*log(3*x)^2)^3 + 6*(2*x^14 +
16*x^13 + 32*x^12 + (8*x^15 + 61*x^14 + 120*x^13 + 16*x^12)*log(3*x))*log(x*log(3*x)^2)^2 + 2*(6*x^15 + 48*x^1
4 + 96*x^13 + (17*x^16 + 131*x^15 + 264*x^14 + 48*x^13)*log(3*x))*log(x*log(3*x)^2) + (9*x^17 + 70*x^16 + 144*
x^15 + 32*x^14)*log(3*x))/log(3*x), x)

Mupad [B] (verification not implemented)

Time = 13.00 (sec) , antiderivative size = 122, normalized size of antiderivative = 5.55 \[ \int \frac {128 x^{14}+64 x^{15}+8 x^{16}+\left (64 x^{14}+288 x^{15}+140 x^{16}+18 x^{17}\right ) \log (3 x)+\left (384 x^{13}+192 x^{14}+24 x^{15}+\left (192 x^{13}+1056 x^{14}+524 x^{15}+68 x^{16}\right ) \log (3 x)\right ) \log \left (x \log ^2(3 x)\right )+\left (384 x^{12}+192 x^{13}+24 x^{14}+\left (192 x^{12}+1440 x^{13}+732 x^{14}+96 x^{15}\right ) \log (3 x)\right ) \log ^2\left (x \log ^2(3 x)\right )+\left (128 x^{11}+64 x^{12}+8 x^{13}+\left (64 x^{11}+864 x^{12}+452 x^{13}+60 x^{14}\right ) \log (3 x)\right ) \log ^3\left (x \log ^2(3 x)\right )+\left (192 x^{11}+104 x^{12}+14 x^{13}\right ) \log (3 x) \log ^4\left (x \log ^2(3 x)\right )}{\log (3 x)} \, dx=\ln \left (x\,{\ln \left (3\,x\right )}^2\right )\,\left (4\,x^{17}+32\,x^{16}+64\,x^{15}\right )+{\ln \left (x\,{\ln \left (3\,x\right )}^2\right )}^4\,\left (x^{14}+8\,x^{13}+16\,x^{12}\right )+{\ln \left (x\,{\ln \left (3\,x\right )}^2\right )}^3\,\left (4\,x^{15}+32\,x^{14}+64\,x^{13}\right )+{\ln \left (x\,{\ln \left (3\,x\right )}^2\right )}^2\,\left (6\,x^{16}+48\,x^{15}+96\,x^{14}\right )+16\,x^{16}+8\,x^{17}+x^{18} \]

[In]

int((log(x*log(3*x)^2)*(384*x^13 + 192*x^14 + 24*x^15 + log(3*x)*(192*x^13 + 1056*x^14 + 524*x^15 + 68*x^16))
+ log(x*log(3*x)^2)^3*(128*x^11 + 64*x^12 + 8*x^13 + log(3*x)*(64*x^11 + 864*x^12 + 452*x^13 + 60*x^14)) + log
(x*log(3*x)^2)^2*(384*x^12 + 192*x^13 + 24*x^14 + log(3*x)*(192*x^12 + 1440*x^13 + 732*x^14 + 96*x^15)) + 128*
x^14 + 64*x^15 + 8*x^16 + log(3*x)*(64*x^14 + 288*x^15 + 140*x^16 + 18*x^17) + log(3*x)*log(x*log(3*x)^2)^4*(1
92*x^11 + 104*x^12 + 14*x^13))/log(3*x),x)

[Out]

log(x*log(3*x)^2)*(64*x^15 + 32*x^16 + 4*x^17) + log(x*log(3*x)^2)^4*(16*x^12 + 8*x^13 + x^14) + log(x*log(3*x
)^2)^3*(64*x^13 + 32*x^14 + 4*x^15) + log(x*log(3*x)^2)^2*(96*x^14 + 48*x^15 + 6*x^16) + 16*x^16 + 8*x^17 + x^
18