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

Optimal. Leaf size=22 \[ x^{12} (4+x)^2 \left (x+\log \left (x \log ^2(3 x)\right )\right )^4 \]

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Rubi [F]  time = 180.01, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[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]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.68, size = 22, normalized size = 1.00 \begin {gather*} x^{12} (4+x)^2 \left (x+\log \left (x \log ^2(3 x)\right )\right )^4 \end {gather*}

Antiderivative was successfully verified.

[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

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fricas [B]  time = 0.66, size = 119, normalized size = 5.41 \begin {gather*} 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 ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \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} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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maple [F]  time = 0.02, size = 0, normalized size = 0.00 \[\int \frac {\left (14 x^{13}+104 x^{12}+192 x^{11}\right ) \ln \left (3 x \right ) \ln \left (x \ln \left (3 x \right )^{2}\right )^{4}+\left (\left (60 x^{14}+452 x^{13}+864 x^{12}+64 x^{11}\right ) \ln \left (3 x \right )+8 x^{13}+64 x^{12}+128 x^{11}\right ) \ln \left (x \ln \left (3 x \right )^{2}\right )^{3}+\left (\left (96 x^{15}+732 x^{14}+1440 x^{13}+192 x^{12}\right ) \ln \left (3 x \right )+24 x^{14}+192 x^{13}+384 x^{12}\right ) \ln \left (x \ln \left (3 x \right )^{2}\right )^{2}+\left (\left (68 x^{16}+524 x^{15}+1056 x^{14}+192 x^{13}\right ) \ln \left (3 x \right )+24 x^{15}+192 x^{14}+384 x^{13}\right ) \ln \left (x \ln \left (3 x \right )^{2}\right )+\left (18 x^{17}+140 x^{16}+288 x^{15}+64 x^{14}\right ) \ln \left (3 x \right )+8 x^{16}+64 x^{15}+128 x^{14}}{\ln \left (3 x \right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[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)

[Out]

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)

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} x^{18} + 8 \, x^{17} + 16 \, x^{16} + {\left (x^{14} + 8 \, x^{13} + 16 \, x^{12}\right )} \log \relax (x)^{4} + 16 \, {\left (x^{14} + 8 \, x^{13} + 16 \, x^{12}\right )} \log \left (\log \relax (3) + \log \relax (x)\right )^{4} + 4 \, {\left (x^{15} + 8 \, x^{14} + 16 \, x^{13}\right )} \log \relax (x)^{3} + 32 \, {\left (x^{15} + 8 \, x^{14} + 16 \, x^{13} + {\left (x^{14} + 8 \, x^{13} + 16 \, x^{12}\right )} \log \relax (x)\right )} \log \left (\log \relax (3) + \log \relax (x)\right )^{3} + 6 \, {\left (x^{16} + 8 \, x^{15} + 16 \, x^{14}\right )} \log \relax (x)^{2} + 24 \, {\left (x^{16} + 8 \, x^{15} + 16 \, x^{14} + {\left (x^{14} + 8 \, x^{13} + 16 \, x^{12}\right )} \log \relax (x)^{2} + 2 \, {\left (x^{15} + 8 \, x^{14} + 16 \, x^{13}\right )} \log \relax (x)\right )} \log \left (\log \relax (3) + \log \relax (x)\right )^{2} + 4 \, {\left (x^{17} + 8 \, x^{16} + 16 \, x^{15}\right )} \log \relax (x) + 8 \, {\left (x^{17} + 8 \, x^{16} + 16 \, x^{15} + {\left (x^{14} + 8 \, x^{13} + 16 \, x^{12}\right )} \log \relax (x)^{3} + 3 \, {\left (x^{15} + 8 \, x^{14} + 16 \, x^{13}\right )} \log \relax (x)^{2} + 3 \, {\left (x^{16} + 8 \, x^{15} + 16 \, x^{14}\right )} \log \relax (x)\right )} \log \left (\log \relax (3) + \log \relax (x)\right ) + \frac {8}{129140163} \, {\rm Ei}\left (17 \, \log \left (3 \, x\right )\right ) + \frac {64}{43046721} \, {\rm Ei}\left (16 \, \log \left (3 \, x\right )\right ) + \frac {128}{14348907} \, {\rm Ei}\left (15 \, \log \left (3 \, x\right )\right ) - 2 \, \int \frac {4 \, {\left (x^{16} + 8 \, x^{15} + 16 \, x^{14}\right )}}{\log \relax (3) + \log \relax (x)}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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mupad [B]  time = 7.37, size = 122, normalized size = 5.55 \begin {gather*} \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} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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

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sympy [B]  time = 0.89, size = 117, normalized size = 5.32 \begin {gather*} 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 )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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