3.30.55 \(\int \frac {e^{\frac {6561+5832 x^2-2916 x^3+1944 x^4-1944 x^5+774 x^6-432 x^7+232 x^8+e^4 x^8+e^5 x^8-68 x^9+24 x^{10}-8 x^{11}+x^{12}+e^2 (162 x^4+72 x^6-36 x^7+8 x^8-8 x^9+2 x^{10})+(-2916 x^2-1944 x^4+972 x^5-432 x^6+432 x^7-140 x^8+48 x^9-24 x^{10}+4 x^{11}+e^2 (-36 x^6-8 x^8+4 x^9)) \log (x)+(486 x^4+216 x^6-108 x^7+24 x^8+2 e^2 x^8-24 x^9+6 x^{10}) \log ^2(x)+(-36 x^6-8 x^8+4 x^9) \log ^3(x)+x^8 \log ^4(x)}{x^8}} (-52488-37908 x^2+14580 x^3-9720 x^4+6804 x^5-1980 x^6+864 x^7-140 x^8-20 x^9+24 x^{10}-20 x^{11}+4 x^{12}+e^2 (-648 x^4-180 x^6+36 x^7-8 x^8-4 x^9+4 x^{10})+(17496 x^2+8748 x^4-2916 x^5+1296 x^6-648 x^7+48 x^8-36 x^{10}+12 x^{11}+e^2 (72 x^6+4 x^8+4 x^9)) \log (x)+(-1944 x^4-540 x^6+108 x^7-24 x^8-12 x^9+12 x^{10}) \log ^2(x)+(72 x^6+4 x^8+4 x^9) \log ^3(x))}{x^9} \, dx\)
Optimal. Leaf size=30 \[ -1+e^{e^5+\left (e^2+\left (2+\frac {9}{x^2}-x-\log (x)\right )^2\right )^2} \]
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Rubi [F] time = 180.00, 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[(E^((6561 + 5832*x^2 - 2916*x^3 + 1944*x^4 - 1944*x^5 + 774*x^6 - 432*x^7 + 232*x^8 + E^4*x^8 + E^5*x^8 -
68*x^9 + 24*x^10 - 8*x^11 + x^12 + E^2*(162*x^4 + 72*x^6 - 36*x^7 + 8*x^8 - 8*x^9 + 2*x^10) + (-2916*x^2 - 194
4*x^4 + 972*x^5 - 432*x^6 + 432*x^7 - 140*x^8 + 48*x^9 - 24*x^10 + 4*x^11 + E^2*(-36*x^6 - 8*x^8 + 4*x^9))*Log
[x] + (486*x^4 + 216*x^6 - 108*x^7 + 24*x^8 + 2*E^2*x^8 - 24*x^9 + 6*x^10)*Log[x]^2 + (-36*x^6 - 8*x^8 + 4*x^9
)*Log[x]^3 + x^8*Log[x]^4)/x^8)*(-52488 - 37908*x^2 + 14580*x^3 - 9720*x^4 + 6804*x^5 - 1980*x^6 + 864*x^7 - 1
40*x^8 - 20*x^9 + 24*x^10 - 20*x^11 + 4*x^12 + E^2*(-648*x^4 - 180*x^6 + 36*x^7 - 8*x^8 - 4*x^9 + 4*x^10) + (1
7496*x^2 + 8748*x^4 - 2916*x^5 + 1296*x^6 - 648*x^7 + 48*x^8 - 36*x^10 + 12*x^11 + E^2*(72*x^6 + 4*x^8 + 4*x^9
))*Log[x] + (-1944*x^4 - 540*x^6 + 108*x^7 - 24*x^8 - 12*x^9 + 12*x^10)*Log[x]^2 + (72*x^6 + 4*x^8 + 4*x^9)*Lo
g[x]^3))/x^9,x]
[Out]
$Aborted
Rubi steps
Aborted
________________________________________________________________________________________
Mathematica [B] time = 2.49, size = 137, normalized size = 4.57 \begin {gather*} e^{e^4+e^5+\frac {2 e^2 \left (-9-2 x^2+x^3\right )^2}{x^4}+\frac {\left (-9-2 x^2+x^3\right )^4}{x^8}+2 \left (e^2+\frac {3 \left (-9-2 x^2+x^3\right )^2}{x^4}\right ) \log ^2(x)+4 \left (-2-\frac {9}{x^2}+x\right ) \log ^3(x)+\log ^4(x)} x^{\frac {4 \left (-9-2 x^2+x^3\right ) \left (81+36 x^2-18 x^3+\left (4+e^2\right ) x^4-4 x^5+x^6\right )}{x^6}} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(E^((6561 + 5832*x^2 - 2916*x^3 + 1944*x^4 - 1944*x^5 + 774*x^6 - 432*x^7 + 232*x^8 + E^4*x^8 + E^5*
x^8 - 68*x^9 + 24*x^10 - 8*x^11 + x^12 + E^2*(162*x^4 + 72*x^6 - 36*x^7 + 8*x^8 - 8*x^9 + 2*x^10) + (-2916*x^2
- 1944*x^4 + 972*x^5 - 432*x^6 + 432*x^7 - 140*x^8 + 48*x^9 - 24*x^10 + 4*x^11 + E^2*(-36*x^6 - 8*x^8 + 4*x^9
))*Log[x] + (486*x^4 + 216*x^6 - 108*x^7 + 24*x^8 + 2*E^2*x^8 - 24*x^9 + 6*x^10)*Log[x]^2 + (-36*x^6 - 8*x^8 +
4*x^9)*Log[x]^3 + x^8*Log[x]^4)/x^8)*(-52488 - 37908*x^2 + 14580*x^3 - 9720*x^4 + 6804*x^5 - 1980*x^6 + 864*x
^7 - 140*x^8 - 20*x^9 + 24*x^10 - 20*x^11 + 4*x^12 + E^2*(-648*x^4 - 180*x^6 + 36*x^7 - 8*x^8 - 4*x^9 + 4*x^10
) + (17496*x^2 + 8748*x^4 - 2916*x^5 + 1296*x^6 - 648*x^7 + 48*x^8 - 36*x^10 + 12*x^11 + E^2*(72*x^6 + 4*x^8 +
4*x^9))*Log[x] + (-1944*x^4 - 540*x^6 + 108*x^7 - 24*x^8 - 12*x^9 + 12*x^10)*Log[x]^2 + (72*x^6 + 4*x^8 + 4*x
^9)*Log[x]^3))/x^9,x]
[Out]
E^(E^4 + E^5 + (2*E^2*(-9 - 2*x^2 + x^3)^2)/x^4 + (-9 - 2*x^2 + x^3)^4/x^8 + 2*(E^2 + (3*(-9 - 2*x^2 + x^3)^2)
/x^4)*Log[x]^2 + 4*(-2 - 9/x^2 + x)*Log[x]^3 + Log[x]^4)*x^((4*(-9 - 2*x^2 + x^3)*(81 + 36*x^2 - 18*x^3 + (4 +
E^2)*x^4 - 4*x^5 + x^6))/x^6)
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fricas [B] time = 6.65, size = 241, normalized size = 8.03 \begin {gather*} e^{\left (\frac {x^{12} + x^{8} \log \relax (x)^{4} - 8 \, x^{11} + 24 \, x^{10} - 68 \, x^{9} + x^{8} e^{5} + x^{8} e^{4} + 232 \, x^{8} - 432 \, x^{7} + 774 \, x^{6} - 1944 \, x^{5} + 1944 \, x^{4} + 4 \, {\left (x^{9} - 2 \, x^{8} - 9 \, x^{6}\right )} \log \relax (x)^{3} - 2916 \, x^{3} + 2 \, {\left (3 \, x^{10} - 12 \, x^{9} + x^{8} e^{2} + 12 \, x^{8} - 54 \, x^{7} + 108 \, x^{6} + 243 \, x^{4}\right )} \log \relax (x)^{2} + 5832 \, x^{2} + 2 \, {\left (x^{10} - 4 \, x^{9} + 4 \, x^{8} - 18 \, x^{7} + 36 \, x^{6} + 81 \, x^{4}\right )} e^{2} + 4 \, {\left (x^{11} - 6 \, x^{10} + 12 \, x^{9} - 35 \, x^{8} + 108 \, x^{7} - 108 \, x^{6} + 243 \, x^{5} - 486 \, x^{4} - 729 \, x^{2} + {\left (x^{9} - 2 \, x^{8} - 9 \, x^{6}\right )} e^{2}\right )} \log \relax (x) + 6561}{x^{8}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((4*x^9+4*x^8+72*x^6)*log(x)^3+(12*x^10-12*x^9-24*x^8+108*x^7-540*x^6-1944*x^4)*log(x)^2+((4*x^9+4*x
^8+72*x^6)*exp(2)+12*x^11-36*x^10+48*x^8-648*x^7+1296*x^6-2916*x^5+8748*x^4+17496*x^2)*log(x)+(4*x^10-4*x^9-8*
x^8+36*x^7-180*x^6-648*x^4)*exp(2)+4*x^12-20*x^11+24*x^10-20*x^9-140*x^8+864*x^7-1980*x^6+6804*x^5-9720*x^4+14
580*x^3-37908*x^2-52488)*exp((x^8*log(x)^4+(4*x^9-8*x^8-36*x^6)*log(x)^3+(2*x^8*exp(2)+6*x^10-24*x^9+24*x^8-10
8*x^7+216*x^6+486*x^4)*log(x)^2+((4*x^9-8*x^8-36*x^6)*exp(2)+4*x^11-24*x^10+48*x^9-140*x^8+432*x^7-432*x^6+972
*x^5-1944*x^4-2916*x^2)*log(x)+x^8*exp(5)+x^8*exp(2)^2+(2*x^10-8*x^9+8*x^8-36*x^7+72*x^6+162*x^4)*exp(2)+x^12-
8*x^11+24*x^10-68*x^9+232*x^8-432*x^7+774*x^6-1944*x^5+1944*x^4-2916*x^3+5832*x^2+6561)/x^8)/x^9,x, algorithm=
"fricas")
[Out]
e^((x^12 + x^8*log(x)^4 - 8*x^11 + 24*x^10 - 68*x^9 + x^8*e^5 + x^8*e^4 + 232*x^8 - 432*x^7 + 774*x^6 - 1944*x
^5 + 1944*x^4 + 4*(x^9 - 2*x^8 - 9*x^6)*log(x)^3 - 2916*x^3 + 2*(3*x^10 - 12*x^9 + x^8*e^2 + 12*x^8 - 54*x^7 +
108*x^6 + 243*x^4)*log(x)^2 + 5832*x^2 + 2*(x^10 - 4*x^9 + 4*x^8 - 18*x^7 + 36*x^6 + 81*x^4)*e^2 + 4*(x^11 -
6*x^10 + 12*x^9 - 35*x^8 + 108*x^7 - 108*x^6 + 243*x^5 - 486*x^4 - 729*x^2 + (x^9 - 2*x^8 - 9*x^6)*e^2)*log(x)
+ 6561)/x^8)
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giac [B] time = 2.78, size = 258, normalized size = 8.60 \begin {gather*} e^{\left (x^{4} + 4 \, x^{3} \log \relax (x) + 6 \, x^{2} \log \relax (x)^{2} + 4 \, x \log \relax (x)^{3} + \log \relax (x)^{4} - 8 \, x^{3} + 2 \, x^{2} e^{2} - 24 \, x^{2} \log \relax (x) + 4 \, x e^{2} \log \relax (x) - 24 \, x \log \relax (x)^{2} + 2 \, e^{2} \log \relax (x)^{2} - 8 \, \log \relax (x)^{3} + 24 \, x^{2} - 8 \, x e^{2} + 48 \, x \log \relax (x) - 8 \, e^{2} \log \relax (x) + 24 \, \log \relax (x)^{2} - 68 \, x - \frac {108 \, \log \relax (x)^{2}}{x} - \frac {36 \, \log \relax (x)^{3}}{x^{2}} - \frac {36 \, e^{2}}{x} + \frac {432 \, \log \relax (x)}{x} - \frac {36 \, e^{2} \log \relax (x)}{x^{2}} + \frac {216 \, \log \relax (x)^{2}}{x^{2}} - \frac {432}{x} + \frac {72 \, e^{2}}{x^{2}} - \frac {432 \, \log \relax (x)}{x^{2}} + \frac {774}{x^{2}} + \frac {972 \, \log \relax (x)}{x^{3}} + \frac {486 \, \log \relax (x)^{2}}{x^{4}} - \frac {1944}{x^{3}} + \frac {162 \, e^{2}}{x^{4}} - \frac {1944 \, \log \relax (x)}{x^{4}} + \frac {1944}{x^{4}} - \frac {2916}{x^{5}} - \frac {2916 \, \log \relax (x)}{x^{6}} + \frac {5832}{x^{6}} + \frac {6561}{x^{8}} + e^{5} + e^{4} + 8 \, e^{2} - 140 \, \log \relax (x) + 232\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((4*x^9+4*x^8+72*x^6)*log(x)^3+(12*x^10-12*x^9-24*x^8+108*x^7-540*x^6-1944*x^4)*log(x)^2+((4*x^9+4*x
^8+72*x^6)*exp(2)+12*x^11-36*x^10+48*x^8-648*x^7+1296*x^6-2916*x^5+8748*x^4+17496*x^2)*log(x)+(4*x^10-4*x^9-8*
x^8+36*x^7-180*x^6-648*x^4)*exp(2)+4*x^12-20*x^11+24*x^10-20*x^9-140*x^8+864*x^7-1980*x^6+6804*x^5-9720*x^4+14
580*x^3-37908*x^2-52488)*exp((x^8*log(x)^4+(4*x^9-8*x^8-36*x^6)*log(x)^3+(2*x^8*exp(2)+6*x^10-24*x^9+24*x^8-10
8*x^7+216*x^6+486*x^4)*log(x)^2+((4*x^9-8*x^8-36*x^6)*exp(2)+4*x^11-24*x^10+48*x^9-140*x^8+432*x^7-432*x^6+972
*x^5-1944*x^4-2916*x^2)*log(x)+x^8*exp(5)+x^8*exp(2)^2+(2*x^10-8*x^9+8*x^8-36*x^7+72*x^6+162*x^4)*exp(2)+x^12-
8*x^11+24*x^10-68*x^9+232*x^8-432*x^7+774*x^6-1944*x^5+1944*x^4-2916*x^3+5832*x^2+6561)/x^8)/x^9,x, algorithm=
"giac")
[Out]
e^(x^4 + 4*x^3*log(x) + 6*x^2*log(x)^2 + 4*x*log(x)^3 + log(x)^4 - 8*x^3 + 2*x^2*e^2 - 24*x^2*log(x) + 4*x*e^2
*log(x) - 24*x*log(x)^2 + 2*e^2*log(x)^2 - 8*log(x)^3 + 24*x^2 - 8*x*e^2 + 48*x*log(x) - 8*e^2*log(x) + 24*log
(x)^2 - 68*x - 108*log(x)^2/x - 36*log(x)^3/x^2 - 36*e^2/x + 432*log(x)/x - 36*e^2*log(x)/x^2 + 216*log(x)^2/x
^2 - 432/x + 72*e^2/x^2 - 432*log(x)/x^2 + 774/x^2 + 972*log(x)/x^3 + 486*log(x)^2/x^4 - 1944/x^3 + 162*e^2/x^
4 - 1944*log(x)/x^4 + 1944/x^4 - 2916/x^5 - 2916*log(x)/x^6 + 5832/x^6 + 6561/x^8 + e^5 + e^4 + 8*e^2 - 140*lo
g(x) + 232)
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maple [B] time = 0.10, size = 295, normalized size = 9.83
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| method |
result |
size |
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| risch |
\(\frac {x^{-24 x^{2}} x^{4 \,{\mathrm e}^{2} x} x^{\frac {432}{x}} x^{4 x^{3}} x^{-8 \,{\mathrm e}^{2}} x^{-\frac {432}{x^{2}}} x^{48 x} x^{\frac {972}{x^{3}}} x^{-\frac {1944}{x^{4}}} x^{-\frac {2916}{x^{6}}} x^{-\frac {36 \,{\mathrm e}^{2}}{x^{2}}} {\mathrm e}^{\frac {6561-8 x^{8} \ln \relax (x )^{3}-24 x^{9} \ln \relax (x )^{2}-108 x^{7} \ln \relax (x )^{2}+4 x^{9} \ln \relax (x )^{3}+6 x^{10} \ln \relax (x )^{2}-8 x^{11}+x^{12}-432 x^{7}+232 x^{8}+24 x^{10}-68 x^{9}+774 x^{6}-1944 x^{5}+1944 x^{4}-2916 x^{3}+5832 x^{2}+72 x^{6} {\mathrm e}^{2}+24 x^{8} \ln \relax (x )^{2}+216 x^{6} \ln \relax (x )^{2}+8 x^{8} {\mathrm e}^{2}-36 x^{6} \ln \relax (x )^{3}+x^{8} {\mathrm e}^{4}+486 x^{4} \ln \relax (x )^{2}+x^{8} {\mathrm e}^{5}+162 x^{4} {\mathrm e}^{2}+x^{8} \ln \relax (x )^{4}+2 \,{\mathrm e}^{2} x^{10}-8 \,{\mathrm e}^{2} x^{9}-36 x^{7} {\mathrm e}^{2}+2 \,{\mathrm e}^{2} \ln \relax (x )^{2} x^{8}}{x^{8}}}}{x^{140}}\) |
\(295\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((4*x^9+4*x^8+72*x^6)*ln(x)^3+(12*x^10-12*x^9-24*x^8+108*x^7-540*x^6-1944*x^4)*ln(x)^2+((4*x^9+4*x^8+72*x^
6)*exp(2)+12*x^11-36*x^10+48*x^8-648*x^7+1296*x^6-2916*x^5+8748*x^4+17496*x^2)*ln(x)+(4*x^10-4*x^9-8*x^8+36*x^
7-180*x^6-648*x^4)*exp(2)+4*x^12-20*x^11+24*x^10-20*x^9-140*x^8+864*x^7-1980*x^6+6804*x^5-9720*x^4+14580*x^3-3
7908*x^2-52488)*exp((x^8*ln(x)^4+(4*x^9-8*x^8-36*x^6)*ln(x)^3+(2*x^8*exp(2)+6*x^10-24*x^9+24*x^8-108*x^7+216*x
^6+486*x^4)*ln(x)^2+((4*x^9-8*x^8-36*x^6)*exp(2)+4*x^11-24*x^10+48*x^9-140*x^8+432*x^7-432*x^6+972*x^5-1944*x^
4-2916*x^2)*ln(x)+x^8*exp(5)+x^8*exp(2)^2+(2*x^10-8*x^9+8*x^8-36*x^7+72*x^6+162*x^4)*exp(2)+x^12-8*x^11+24*x^1
0-68*x^9+232*x^8-432*x^7+774*x^6-1944*x^5+1944*x^4-2916*x^3+5832*x^2+6561)/x^8)/x^9,x,method=_RETURNVERBOSE)
[Out]
x^(-24*x^2)*x^(4*exp(2)*x)*x^(432/x)/x^140*x^(4*x^3)*x^(-8*exp(2))*x^(-432/x^2)*x^(48*x)*x^(972/x^3)*x^(-1944/
x^4)*x^(-2916/x^6)*x^(-36*exp(2)/x^2)*exp((6561-8*x^8*ln(x)^3-24*x^9*ln(x)^2-108*x^7*ln(x)^2+4*x^9*ln(x)^3+6*x
^10*ln(x)^2-8*x^11+x^12-432*x^7+232*x^8+24*x^10-68*x^9+774*x^6-1944*x^5+1944*x^4-2916*x^3+5832*x^2+72*x^6*exp(
2)+24*x^8*ln(x)^2+216*x^6*ln(x)^2+8*x^8*exp(2)-36*x^6*ln(x)^3+x^8*exp(4)+486*x^4*ln(x)^2+x^8*exp(5)+162*x^4*ex
p(2)+x^8*ln(x)^4+2*exp(2)*x^10-8*exp(2)*x^9-36*x^7*exp(2)+2*exp(2)*ln(x)^2*x^8)/x^8)
________________________________________________________________________________________
maxima [B] time = 9.77, size = 258, normalized size = 8.60 \begin {gather*} \frac {e^{\left (x^{4} + 4 \, x^{3} \log \relax (x) + 6 \, x^{2} \log \relax (x)^{2} + 4 \, x \log \relax (x)^{3} + \log \relax (x)^{4} - 8 \, x^{3} + 2 \, x^{2} e^{2} - 24 \, x^{2} \log \relax (x) + 4 \, x e^{2} \log \relax (x) - 24 \, x \log \relax (x)^{2} + 2 \, e^{2} \log \relax (x)^{2} - 8 \, \log \relax (x)^{3} + 24 \, x^{2} - 8 \, x e^{2} + 48 \, x \log \relax (x) - 8 \, e^{2} \log \relax (x) + 24 \, \log \relax (x)^{2} - 68 \, x - \frac {108 \, \log \relax (x)^{2}}{x} - \frac {36 \, \log \relax (x)^{3}}{x^{2}} - \frac {36 \, e^{2}}{x} + \frac {432 \, \log \relax (x)}{x} - \frac {36 \, e^{2} \log \relax (x)}{x^{2}} + \frac {216 \, \log \relax (x)^{2}}{x^{2}} - \frac {432}{x} + \frac {72 \, e^{2}}{x^{2}} - \frac {432 \, \log \relax (x)}{x^{2}} + \frac {774}{x^{2}} + \frac {972 \, \log \relax (x)}{x^{3}} + \frac {486 \, \log \relax (x)^{2}}{x^{4}} - \frac {1944}{x^{3}} + \frac {162 \, e^{2}}{x^{4}} - \frac {1944 \, \log \relax (x)}{x^{4}} + \frac {1944}{x^{4}} - \frac {2916}{x^{5}} - \frac {2916 \, \log \relax (x)}{x^{6}} + \frac {5832}{x^{6}} + \frac {6561}{x^{8}} + e^{5} + e^{4} + 8 \, e^{2} + 232\right )}}{x^{140}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((4*x^9+4*x^8+72*x^6)*log(x)^3+(12*x^10-12*x^9-24*x^8+108*x^7-540*x^6-1944*x^4)*log(x)^2+((4*x^9+4*x
^8+72*x^6)*exp(2)+12*x^11-36*x^10+48*x^8-648*x^7+1296*x^6-2916*x^5+8748*x^4+17496*x^2)*log(x)+(4*x^10-4*x^9-8*
x^8+36*x^7-180*x^6-648*x^4)*exp(2)+4*x^12-20*x^11+24*x^10-20*x^9-140*x^8+864*x^7-1980*x^6+6804*x^5-9720*x^4+14
580*x^3-37908*x^2-52488)*exp((x^8*log(x)^4+(4*x^9-8*x^8-36*x^6)*log(x)^3+(2*x^8*exp(2)+6*x^10-24*x^9+24*x^8-10
8*x^7+216*x^6+486*x^4)*log(x)^2+((4*x^9-8*x^8-36*x^6)*exp(2)+4*x^11-24*x^10+48*x^9-140*x^8+432*x^7-432*x^6+972
*x^5-1944*x^4-2916*x^2)*log(x)+x^8*exp(5)+x^8*exp(2)^2+(2*x^10-8*x^9+8*x^8-36*x^7+72*x^6+162*x^4)*exp(2)+x^12-
8*x^11+24*x^10-68*x^9+232*x^8-432*x^7+774*x^6-1944*x^5+1944*x^4-2916*x^3+5832*x^2+6561)/x^8)/x^9,x, algorithm=
"maxima")
[Out]
e^(x^4 + 4*x^3*log(x) + 6*x^2*log(x)^2 + 4*x*log(x)^3 + log(x)^4 - 8*x^3 + 2*x^2*e^2 - 24*x^2*log(x) + 4*x*e^2
*log(x) - 24*x*log(x)^2 + 2*e^2*log(x)^2 - 8*log(x)^3 + 24*x^2 - 8*x*e^2 + 48*x*log(x) - 8*e^2*log(x) + 24*log
(x)^2 - 68*x - 108*log(x)^2/x - 36*log(x)^3/x^2 - 36*e^2/x + 432*log(x)/x - 36*e^2*log(x)/x^2 + 216*log(x)^2/x
^2 - 432/x + 72*e^2/x^2 - 432*log(x)/x^2 + 774/x^2 + 972*log(x)/x^3 + 486*log(x)^2/x^4 - 1944/x^3 + 162*e^2/x^
4 - 1944*log(x)/x^4 + 1944/x^4 - 2916/x^5 - 2916*log(x)/x^6 + 5832/x^6 + 6561/x^8 + e^5 + e^4 + 8*e^2 + 232)/x
^140
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mupad [B] time = 3.04, size = 299, normalized size = 9.97 \begin {gather*} \frac {x^{4\,x^3}\,x^{432/x}\,x^{\frac {972}{x^3}}\,x^{4\,x\,{\mathrm {e}}^2}\,x^{48\,x}\,{\mathrm {e}}^{2\,x^2\,{\mathrm {e}}^2}\,{\mathrm {e}}^{-\frac {36\,{\mathrm {e}}^2}{x}}\,{\mathrm {e}}^{\frac {72\,{\mathrm {e}}^2}{x^2}}\,{\mathrm {e}}^{\frac {162\,{\mathrm {e}}^2}{x^4}}\,{\mathrm {e}}^{-8\,{\ln \relax (x)}^3}\,{\mathrm {e}}^{24\,{\ln \relax (x)}^2}\,{\mathrm {e}}^{8\,{\mathrm {e}}^2}\,{\mathrm {e}}^{-68\,x}\,{\mathrm {e}}^{x^4}\,{\mathrm {e}}^{232}\,{\mathrm {e}}^{2\,{\mathrm {e}}^2\,{\ln \relax (x)}^2}\,{\mathrm {e}}^{4\,x\,{\ln \relax (x)}^3}\,{\mathrm {e}}^{-24\,x\,{\ln \relax (x)}^2}\,{\mathrm {e}}^{-8\,x^3}\,{\mathrm {e}}^{24\,x^2}\,{\mathrm {e}}^{-\frac {432}{x}}\,{\mathrm {e}}^{\frac {774}{x^2}}\,{\mathrm {e}}^{-\frac {1944}{x^3}}\,{\mathrm {e}}^{\frac {1944}{x^4}}\,{\mathrm {e}}^{-\frac {2916}{x^5}}\,{\mathrm {e}}^{\frac {5832}{x^6}}\,{\mathrm {e}}^{\frac {6561}{x^8}}\,{\mathrm {e}}^{-8\,x\,{\mathrm {e}}^2}\,{\mathrm {e}}^{{\ln \relax (x)}^4}\,{\mathrm {e}}^{{\mathrm {e}}^4}\,{\mathrm {e}}^{{\mathrm {e}}^5}\,{\mathrm {e}}^{6\,x^2\,{\ln \relax (x)}^2}\,{\mathrm {e}}^{-\frac {36\,{\ln \relax (x)}^3}{x^2}}\,{\mathrm {e}}^{-\frac {108\,{\ln \relax (x)}^2}{x}}\,{\mathrm {e}}^{\frac {216\,{\ln \relax (x)}^2}{x^2}}\,{\mathrm {e}}^{\frac {486\,{\ln \relax (x)}^2}{x^4}}}{x^{24\,x^2}\,x^{\frac {432}{x^2}}\,x^{\frac {1944}{x^4}}\,x^{\frac {2916}{x^6}}\,x^{\frac {36\,{\mathrm {e}}^2}{x^2}}\,x^{8\,{\mathrm {e}}^2}\,x^{140}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(-(exp((exp(2)*(162*x^4 + 72*x^6 - 36*x^7 + 8*x^8 - 8*x^9 + 2*x^10) - log(x)*(exp(2)*(36*x^6 + 8*x^8 - 4*x^
9) + 2916*x^2 + 1944*x^4 - 972*x^5 + 432*x^6 - 432*x^7 + 140*x^8 - 48*x^9 + 24*x^10 - 4*x^11) + x^8*log(x)^4 +
x^8*exp(4) + x^8*exp(5) - log(x)^3*(36*x^6 + 8*x^8 - 4*x^9) + 5832*x^2 - 2916*x^3 + 1944*x^4 - 1944*x^5 + 774
*x^6 - 432*x^7 + 232*x^8 - 68*x^9 + 24*x^10 - 8*x^11 + x^12 + log(x)^2*(2*x^8*exp(2) + 486*x^4 + 216*x^6 - 108
*x^7 + 24*x^8 - 24*x^9 + 6*x^10) + 6561)/x^8)*(log(x)^2*(1944*x^4 + 540*x^6 - 108*x^7 + 24*x^8 + 12*x^9 - 12*x
^10) - log(x)*(exp(2)*(72*x^6 + 4*x^8 + 4*x^9) + 17496*x^2 + 8748*x^4 - 2916*x^5 + 1296*x^6 - 648*x^7 + 48*x^8
- 36*x^10 + 12*x^11) + exp(2)*(648*x^4 + 180*x^6 - 36*x^7 + 8*x^8 + 4*x^9 - 4*x^10) - log(x)^3*(72*x^6 + 4*x^
8 + 4*x^9) + 37908*x^2 - 14580*x^3 + 9720*x^4 - 6804*x^5 + 1980*x^6 - 864*x^7 + 140*x^8 + 20*x^9 - 24*x^10 + 2
0*x^11 - 4*x^12 + 52488))/x^9,x)
[Out]
(x^(4*x^3)*x^(432/x)*x^(972/x^3)*x^(4*x*exp(2))*x^(48*x)*exp(2*x^2*exp(2))*exp(-(36*exp(2))/x)*exp((72*exp(2))
/x^2)*exp((162*exp(2))/x^4)*exp(-8*log(x)^3)*exp(24*log(x)^2)*exp(8*exp(2))*exp(-68*x)*exp(x^4)*exp(232)*exp(2
*exp(2)*log(x)^2)*exp(4*x*log(x)^3)*exp(-24*x*log(x)^2)*exp(-8*x^3)*exp(24*x^2)*exp(-432/x)*exp(774/x^2)*exp(-
1944/x^3)*exp(1944/x^4)*exp(-2916/x^5)*exp(5832/x^6)*exp(6561/x^8)*exp(-8*x*exp(2))*exp(log(x)^4)*exp(exp(4))*
exp(exp(5))*exp(6*x^2*log(x)^2)*exp(-(36*log(x)^3)/x^2)*exp(-(108*log(x)^2)/x)*exp((216*log(x)^2)/x^2)*exp((48
6*log(x)^2)/x^4))/(x^(24*x^2)*x^(432/x^2)*x^(1944/x^4)*x^(2916/x^6)*x^((36*exp(2))/x^2)*x^(8*exp(2))*x^140)
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sympy [B] time = 4.77, size = 248, normalized size = 8.27 \begin {gather*} e^{\frac {x^{12} - 8 x^{11} + 24 x^{10} - 68 x^{9} + x^{8} \log {\relax (x )}^{4} + x^{8} e^{4} + x^{8} e^{5} + 232 x^{8} - 432 x^{7} + 774 x^{6} - 1944 x^{5} + 1944 x^{4} - 2916 x^{3} + 5832 x^{2} + \left (4 x^{9} - 8 x^{8} - 36 x^{6}\right ) \log {\relax (x )}^{3} + \left (2 x^{10} - 8 x^{9} + 8 x^{8} - 36 x^{7} + 72 x^{6} + 162 x^{4}\right ) e^{2} + \left (6 x^{10} - 24 x^{9} + 2 x^{8} e^{2} + 24 x^{8} - 108 x^{7} + 216 x^{6} + 486 x^{4}\right ) \log {\relax (x )}^{2} + \left (4 x^{11} - 24 x^{10} + 48 x^{9} - 140 x^{8} + 432 x^{7} - 432 x^{6} + 972 x^{5} - 1944 x^{4} - 2916 x^{2} + \left (4 x^{9} - 8 x^{8} - 36 x^{6}\right ) e^{2}\right ) \log {\relax (x )} + 6561}{x^{8}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((4*x**9+4*x**8+72*x**6)*ln(x)**3+(12*x**10-12*x**9-24*x**8+108*x**7-540*x**6-1944*x**4)*ln(x)**2+((
4*x**9+4*x**8+72*x**6)*exp(2)+12*x**11-36*x**10+48*x**8-648*x**7+1296*x**6-2916*x**5+8748*x**4+17496*x**2)*ln(
x)+(4*x**10-4*x**9-8*x**8+36*x**7-180*x**6-648*x**4)*exp(2)+4*x**12-20*x**11+24*x**10-20*x**9-140*x**8+864*x**
7-1980*x**6+6804*x**5-9720*x**4+14580*x**3-37908*x**2-52488)*exp((x**8*ln(x)**4+(4*x**9-8*x**8-36*x**6)*ln(x)*
*3+(2*x**8*exp(2)+6*x**10-24*x**9+24*x**8-108*x**7+216*x**6+486*x**4)*ln(x)**2+((4*x**9-8*x**8-36*x**6)*exp(2)
+4*x**11-24*x**10+48*x**9-140*x**8+432*x**7-432*x**6+972*x**5-1944*x**4-2916*x**2)*ln(x)+x**8*exp(5)+x**8*exp(
2)**2+(2*x**10-8*x**9+8*x**8-36*x**7+72*x**6+162*x**4)*exp(2)+x**12-8*x**11+24*x**10-68*x**9+232*x**8-432*x**7
+774*x**6-1944*x**5+1944*x**4-2916*x**3+5832*x**2+6561)/x**8)/x**9,x)
[Out]
exp((x**12 - 8*x**11 + 24*x**10 - 68*x**9 + x**8*log(x)**4 + x**8*exp(4) + x**8*exp(5) + 232*x**8 - 432*x**7 +
774*x**6 - 1944*x**5 + 1944*x**4 - 2916*x**3 + 5832*x**2 + (4*x**9 - 8*x**8 - 36*x**6)*log(x)**3 + (2*x**10 -
8*x**9 + 8*x**8 - 36*x**7 + 72*x**6 + 162*x**4)*exp(2) + (6*x**10 - 24*x**9 + 2*x**8*exp(2) + 24*x**8 - 108*x
**7 + 216*x**6 + 486*x**4)*log(x)**2 + (4*x**11 - 24*x**10 + 48*x**9 - 140*x**8 + 432*x**7 - 432*x**6 + 972*x*
*5 - 1944*x**4 - 2916*x**2 + (4*x**9 - 8*x**8 - 36*x**6)*exp(2))*log(x) + 6561)/x**8)
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