3.84.24 \(\int \frac {1}{3} e^{-4+\frac {e^{33 x} x^2+8 e^{29 x} x^2 \log (x)+28 e^{25 x} x^2 \log ^2(x)+56 e^{21 x} x^2 \log ^3(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{13 x} x^2 \log ^5(x)+28 e^{9 x} x^2 \log ^6(x)+8 e^{5 x} x^2 \log ^7(x)+e^x x^2 \log ^8(x)}{3 e^4}} (8 e^{29 x} x+e^{33 x} (2 x+33 x^2)+(56 e^{25 x} x+e^{29 x} (16 x+232 x^2)) \log (x)+(168 e^{21 x} x+e^{25 x} (56 x+700 x^2)) \log ^2(x)+(280 e^{17 x} x+e^{21 x} (112 x+1176 x^2)) \log ^3(x)+(280 e^{13 x} x+e^{17 x} (140 x+1190 x^2)) \log ^4(x)+(168 e^{9 x} x+e^{13 x} (112 x+728 x^2)) \log ^5(x)+(56 e^{5 x} x+e^{9 x} (56 x+252 x^2)) \log ^6(x)+(8 e^x x+e^{5 x} (16 x+40 x^2)) \log ^7(x)+e^x (2 x+x^2) \log ^8(x)) \, dx\) [8324]

Optimal. Leaf size=24 \[ e^{\frac {1}{3} e^{-4+x} x^2 \left (e^{4 x}+\log (x)\right )^8} \]

[Out]

exp(1/3*exp(x)/exp(4)*(ln(x)+exp(2*x)^2)^8*x^2)

________________________________________________________________________________________

Rubi [F]
time = 178.73, 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*} \int \frac {1}{3} \exp \left (-4+\frac {e^{33 x} x^2+8 e^{29 x} x^2 \log (x)+28 e^{25 x} x^2 \log ^2(x)+56 e^{21 x} x^2 \log ^3(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{13 x} x^2 \log ^5(x)+28 e^{9 x} x^2 \log ^6(x)+8 e^{5 x} x^2 \log ^7(x)+e^x x^2 \log ^8(x)}{3 e^4}\right ) \left (8 e^{29 x} x+e^{33 x} \left (2 x+33 x^2\right )+\left (56 e^{25 x} x+e^{29 x} \left (16 x+232 x^2\right )\right ) \log (x)+\left (168 e^{21 x} x+e^{25 x} \left (56 x+700 x^2\right )\right ) \log ^2(x)+\left (280 e^{17 x} x+e^{21 x} \left (112 x+1176 x^2\right )\right ) \log ^3(x)+\left (280 e^{13 x} x+e^{17 x} \left (140 x+1190 x^2\right )\right ) \log ^4(x)+\left (168 e^{9 x} x+e^{13 x} \left (112 x+728 x^2\right )\right ) \log ^5(x)+\left (56 e^{5 x} x+e^{9 x} \left (56 x+252 x^2\right )\right ) \log ^6(x)+\left (8 e^x x+e^{5 x} \left (16 x+40 x^2\right )\right ) \log ^7(x)+e^x \left (2 x+x^2\right ) \log ^8(x)\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(-4 + (E^(33*x)*x^2 + 8*E^(29*x)*x^2*Log[x] + 28*E^(25*x)*x^2*Log[x]^2 + 56*E^(21*x)*x^2*Log[x]^3 + 70*
E^(17*x)*x^2*Log[x]^4 + 56*E^(13*x)*x^2*Log[x]^5 + 28*E^(9*x)*x^2*Log[x]^6 + 8*E^(5*x)*x^2*Log[x]^7 + E^x*x^2*
Log[x]^8)/(3*E^4))*(8*E^(29*x)*x + E^(33*x)*(2*x + 33*x^2) + (56*E^(25*x)*x + E^(29*x)*(16*x + 232*x^2))*Log[x
] + (168*E^(21*x)*x + E^(25*x)*(56*x + 700*x^2))*Log[x]^2 + (280*E^(17*x)*x + E^(21*x)*(112*x + 1176*x^2))*Log
[x]^3 + (280*E^(13*x)*x + E^(17*x)*(140*x + 1190*x^2))*Log[x]^4 + (168*E^(9*x)*x + E^(13*x)*(112*x + 728*x^2))
*Log[x]^5 + (56*E^(5*x)*x + E^(9*x)*(56*x + 252*x^2))*Log[x]^6 + (8*E^x*x + E^(5*x)*(16*x + 40*x^2))*Log[x]^7
+ E^x*(2*x + x^2)*Log[x]^8))/3,x]

[Out]

(8*Defer[Int][E^((-12*E^4 + 87*E^4*x + E^(33*x)*x^2 + 28*E^(25*x)*x^2*Log[x]^2 + 56*E^(21*x)*x^2*Log[x]^3 + 70
*E^(17*x)*x^2*Log[x]^4 + 56*E^(13*x)*x^2*Log[x]^5 + 28*E^(9*x)*x^2*Log[x]^6 + 8*E^(5*x)*x^2*Log[x]^7 + E^x*x^2
*Log[x]^8)/(3*E^4))*x^(1 + (8*E^(-4 + 29*x)*x^2)/3), x])/3 + (2*Defer[Int][E^((-12*E^4 + 99*E^4*x + E^(33*x)*x
^2 + 28*E^(25*x)*x^2*Log[x]^2 + 56*E^(21*x)*x^2*Log[x]^3 + 70*E^(17*x)*x^2*Log[x]^4 + 56*E^(13*x)*x^2*Log[x]^5
+ 28*E^(9*x)*x^2*Log[x]^6 + 8*E^(5*x)*x^2*Log[x]^7 + E^x*x^2*Log[x]^8)/(3*E^4))*x^(1 + (8*E^(-4 + 29*x)*x^2)/
3), x])/3 + 11*Defer[Int][E^((-12*E^4 + 99*E^4*x + E^(33*x)*x^2 + 28*E^(25*x)*x^2*Log[x]^2 + 56*E^(21*x)*x^2*L
og[x]^3 + 70*E^(17*x)*x^2*Log[x]^4 + 56*E^(13*x)*x^2*Log[x]^5 + 28*E^(9*x)*x^2*Log[x]^6 + 8*E^(5*x)*x^2*Log[x]
^7 + E^x*x^2*Log[x]^8)/(3*E^4))*x^(2 + (8*E^(-4 + 29*x)*x^2)/3), x] + (56*Defer[Int][E^((-12*E^4 + 75*E^4*x +
E^(33*x)*x^2 + 28*E^(25*x)*x^2*Log[x]^2 + 56*E^(21*x)*x^2*Log[x]^3 + 70*E^(17*x)*x^2*Log[x]^4 + 56*E^(13*x)*x^
2*Log[x]^5 + 28*E^(9*x)*x^2*Log[x]^6 + 8*E^(5*x)*x^2*Log[x]^7 + E^x*x^2*Log[x]^8)/(3*E^4))*x^(1 + (8*E^(-4 + 2
9*x)*x^2)/3)*Log[x], x])/3 + (16*Defer[Int][E^((-12*E^4 + 87*E^4*x + E^(33*x)*x^2 + 28*E^(25*x)*x^2*Log[x]^2 +
56*E^(21*x)*x^2*Log[x]^3 + 70*E^(17*x)*x^2*Log[x]^4 + 56*E^(13*x)*x^2*Log[x]^5 + 28*E^(9*x)*x^2*Log[x]^6 + 8*
E^(5*x)*x^2*Log[x]^7 + E^x*x^2*Log[x]^8)/(3*E^4))*x^(1 + (8*E^(-4 + 29*x)*x^2)/3)*Log[x], x])/3 + (232*Defer[I
nt][E^((-12*E^4 + 87*E^4*x + E^(33*x)*x^2 + 28*E^(25*x)*x^2*Log[x]^2 + 56*E^(21*x)*x^2*Log[x]^3 + 70*E^(17*x)*
x^2*Log[x]^4 + 56*E^(13*x)*x^2*Log[x]^5 + 28*E^(9*x)*x^2*Log[x]^6 + 8*E^(5*x)*x^2*Log[x]^7 + E^x*x^2*Log[x]^8)
/(3*E^4))*x^(2 + (8*E^(-4 + 29*x)*x^2)/3)*Log[x], x])/3 + 56*Defer[Int][E^((-12*E^4 + 63*E^4*x + E^(33*x)*x^2
+ 28*E^(25*x)*x^2*Log[x]^2 + 56*E^(21*x)*x^2*Log[x]^3 + 70*E^(17*x)*x^2*Log[x]^4 + 56*E^(13*x)*x^2*Log[x]^5 +
28*E^(9*x)*x^2*Log[x]^6 + 8*E^(5*x)*x^2*Log[x]^7 + E^x*x^2*Log[x]^8)/(3*E^4))*x^(1 + (8*E^(-4 + 29*x)*x^2)/3)*
Log[x]^2, x] + (56*Defer[Int][E^((-12*E^4 + 75*E^4*x + E^(33*x)*x^2 + 28*E^(25*x)*x^2*Log[x]^2 + 56*E^(21*x)*x
^2*Log[x]^3 + 70*E^(17*x)*x^2*Log[x]^4 + 56*E^(13*x)*x^2*Log[x]^5 + 28*E^(9*x)*x^2*Log[x]^6 + 8*E^(5*x)*x^2*Lo
g[x]^7 + E^x*x^2*Log[x]^8)/(3*E^4))*x^(1 + (8*E^(-4 + 29*x)*x^2)/3)*Log[x]^2, x])/3 + (700*Defer[Int][E^((-12*
E^4 + 75*E^4*x + E^(33*x)*x^2 + 28*E^(25*x)*x^2*Log[x]^2 + 56*E^(21*x)*x^2*Log[x]^3 + 70*E^(17*x)*x^2*Log[x]^4
+ 56*E^(13*x)*x^2*Log[x]^5 + 28*E^(9*x)*x^2*Log[x]^6 + 8*E^(5*x)*x^2*Log[x]^7 + E^x*x^2*Log[x]^8)/(3*E^4))*x^
(2 + (8*E^(-4 + 29*x)*x^2)/3)*Log[x]^2, x])/3 + (280*Defer[Int][E^((-12*E^4 + 51*E^4*x + E^(33*x)*x^2 + 28*E^(
25*x)*x^2*Log[x]^2 + 56*E^(21*x)*x^2*Log[x]^3 + 70*E^(17*x)*x^2*Log[x]^4 + 56*E^(13*x)*x^2*Log[x]^5 + 28*E^(9*
x)*x^2*Log[x]^6 + 8*E^(5*x)*x^2*Log[x]^7 + E^x*x^2*Log[x]^8)/(3*E^4))*x^(1 + (8*E^(-4 + 29*x)*x^2)/3)*Log[x]^3
, x])/3 + (112*Defer[Int][E^((-12*E^4 + 63*E^4*x + E^(33*x)*x^2 + 28*E^(25*x)*x^2*Log[x]^2 + 56*E^(21*x)*x^2*L
og[x]^3 + 70*E^(17*x)*x^2*Log[x]^4 + 56*E^(13*x)*x^2*Log[x]^5 + 28*E^(9*x)*x^2*Log[x]^6 + 8*E^(5*x)*x^2*Log[x]
^7 + E^x*x^2*Log[x]^8)/(3*E^4))*x^(1 + (8*E^(-4 + 29*x)*x^2)/3)*Log[x]^3, x])/3 + 392*Defer[Int][E^((-12*E^4 +
63*E^4*x + E^(33*x)*x^2 + 28*E^(25*x)*x^2*Log[x]^2 + 56*E^(21*x)*x^2*Log[x]^3 + 70*E^(17*x)*x^2*Log[x]^4 + 56
*E^(13*x)*x^2*Log[x]^5 + 28*E^(9*x)*x^2*Log[x]^6 + 8*E^(5*x)*x^2*Log[x]^7 + E^x*x^2*Log[x]^8)/(3*E^4))*x^(2 +
(8*E^(-4 + 29*x)*x^2)/3)*Log[x]^3, x] + (280*Defer[Int][E^((-12*E^4 + 39*E^4*x + E^(33*x)*x^2 + 28*E^(25*x)*x^
2*Log[x]^2 + 56*E^(21*x)*x^2*Log[x]^3 + 70*E^(17*x)*x^2*Log[x]^4 + 56*E^(13*x)*x^2*Log[x]^5 + 28*E^(9*x)*x^2*L
og[x]^6 + 8*E^(5*x)*x^2*Log[x]^7 + E^x*x^2*Log[x]^8)/(3*E^4))*x^(1 + (8*E^(-4 + 29*x)*x^2)/3)*Log[x]^4, x])/3
+ (140*Defer[Int][E^((-12*E^4 + 51*E^4*x + E^(33*x)*x^2 + 28*E^(25*x)*x^2*Log[x]^2 + 56*E^(21*x)*x^2*Log[x]^3
+ 70*E^(17*x)*x^2*Log[x]^4 + 56*E^(13*x)*x^2*Log[x]^5 + 28*E^(9*x)*x^2*Log[x]^6 + 8*E^(5*x)*x^2*Log[x]^7 + E^x
*x^2*Log[x]^8)/(3*E^4))*x^(1 + (8*E^(-4 + 29*x)*x^2)/3)*Log[x]^4, x])/3 + (1190*Defer[Int][E^((-12*E^4 + 51*E^
4*x + E^(33*x)*x^2 + 28*E^(25*x)*x^2*Log[x]^2 + 56*E^(21*x)*x^2*Log[x]^3 + 70*E^(17*x)*x^2*Log[x]^4 + 56*E^(13
*x)*x^2*Log[x]^5 + 28*E^(9*x)*x^2*Log[x]^6 + 8*E^(5*x)*x^2*Log[x]^7 + E^x*x^2*Log[x]^8)/(3*E^4))*x^(2 + (8*E^(
-4 + 29*x)*x^2)/3)*Log[x]^4, x])/3 + 56*Defer[Int][E^((-12*E^4 + 27*E^4*x + E^(33*x)*x^2 + 28*E^(25*x)*x^2*Log
[x]^2 + 56*E^(21*x)*x^2*Log[x]^3 + 70*E^(17*x)*x^2*Log[x]^4 + 56*E^(13*x)*x^2*Log[x]^5 + 28*E^(9*x)*x^2*Log[x]
^6 + 8*E^(5*x)*x^2*Log[x]^7 + E^x*x^2*Log[x]^8)/(3*E^4))*x^(1 + (8*E^(-4 + 29*x)*x^2)/3)*Log[x]^5, x] + (112*D
efer[Int][E^((-12*E^4 + 39*E^4*x + E^(33*x)*x^2 + 28*E^(25*x)*x^2*Log[x]^2 + 56*E^(21*x)*x^2*Log[x]^3 + 70*E^(
17*x)*x^2*Log[x]^4 + 56*E^(13*x)*x^2*Log[x]^5 + 28*E^(9*x)*x^2*Log[x]^6 + 8*E^(5*x)*x^2*Log[x]^7 + E^x*x^2*Log
[x]^8)/(3*E^4))*x^(1 + (8*E^(-4 + 29*x)*x^2)/3)*Log[x]^5, x])/3 + (728*Defer[Int][E^((-12*E^4 + 39*E^4*x + E^(
33*x)*x^2 + 28*E^(25*x)*x^2*Log[x]^2 + 56*E^(21...

Rubi steps

Aborted

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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(107\) vs. \(2(24)=48\).
time = 0.39, size = 107, normalized size = 4.46 \begin {gather*} e^{\frac {1}{3} e^{-4+x} x^2 \left (e^{32 x}+28 e^{24 x} \log ^2(x)+56 e^{20 x} \log ^3(x)+70 e^{16 x} \log ^4(x)+56 e^{12 x} \log ^5(x)+28 e^{8 x} \log ^6(x)+8 e^{4 x} \log ^7(x)+\log ^8(x)\right )} x^{\frac {8}{3} e^{-4+29 x} x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(-4 + (E^(33*x)*x^2 + 8*E^(29*x)*x^2*Log[x] + 28*E^(25*x)*x^2*Log[x]^2 + 56*E^(21*x)*x^2*Log[x]^3
+ 70*E^(17*x)*x^2*Log[x]^4 + 56*E^(13*x)*x^2*Log[x]^5 + 28*E^(9*x)*x^2*Log[x]^6 + 8*E^(5*x)*x^2*Log[x]^7 + E^
x*x^2*Log[x]^8)/(3*E^4))*(8*E^(29*x)*x + E^(33*x)*(2*x + 33*x^2) + (56*E^(25*x)*x + E^(29*x)*(16*x + 232*x^2))
*Log[x] + (168*E^(21*x)*x + E^(25*x)*(56*x + 700*x^2))*Log[x]^2 + (280*E^(17*x)*x + E^(21*x)*(112*x + 1176*x^2
))*Log[x]^3 + (280*E^(13*x)*x + E^(17*x)*(140*x + 1190*x^2))*Log[x]^4 + (168*E^(9*x)*x + E^(13*x)*(112*x + 728
*x^2))*Log[x]^5 + (56*E^(5*x)*x + E^(9*x)*(56*x + 252*x^2))*Log[x]^6 + (8*E^x*x + E^(5*x)*(16*x + 40*x^2))*Log
[x]^7 + E^x*(2*x + x^2)*Log[x]^8))/3,x]

[Out]

E^((E^(-4 + x)*x^2*(E^(32*x) + 28*E^(24*x)*Log[x]^2 + 56*E^(20*x)*Log[x]^3 + 70*E^(16*x)*Log[x]^4 + 56*E^(12*x
)*Log[x]^5 + 28*E^(8*x)*Log[x]^6 + 8*E^(4*x)*Log[x]^7 + Log[x]^8))/3)*x^((8*E^(-4 + 29*x)*x^2)/3)

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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(88\) vs. \(2(23)=46\).
time = 0.68, size = 89, normalized size = 3.71

method	result	size
risch	\({\mathrm e}^{\frac {x^{2} \left ({\mathrm e}^{x} \ln \left (x \right )^{8}+8 \ln \left (x \right )^{7} {\mathrm e}^{5 x}+28 \ln \left (x \right )^{6} {\mathrm e}^{9 x}+56 \ln \left (x \right )^{5} {\mathrm e}^{13 x}+70 \ln \left (x \right )^{4} {\mathrm e}^{17 x}+56 \ln \left (x \right )^{3} {\mathrm e}^{21 x}+28 \ln \left (x \right )^{2} {\mathrm e}^{25 x}+8 \ln \left (x \right ) {\mathrm e}^{29 x}+{\mathrm e}^{33 x}\right ) {\mathrm e}^{-4}}{3}}\)	\(89\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/3*((x^2+2*x)*exp(x)*ln(x)^8+((40*x^2+16*x)*exp(x)*exp(2*x)^2+8*exp(x)*x)*ln(x)^7+((252*x^2+56*x)*exp(x)*
exp(2*x)^4+56*x*exp(x)*exp(2*x)^2)*ln(x)^6+((728*x^2+112*x)*exp(x)*exp(2*x)^6+168*x*exp(x)*exp(2*x)^4)*ln(x)^5
+((1190*x^2+140*x)*exp(x)*exp(2*x)^8+280*x*exp(x)*exp(2*x)^6)*ln(x)^4+((1176*x^2+112*x)*exp(x)*exp(2*x)^10+280
*x*exp(x)*exp(2*x)^8)*ln(x)^3+((700*x^2+56*x)*exp(x)*exp(2*x)^12+168*x*exp(x)*exp(2*x)^10)*ln(x)^2+((232*x^2+1
6*x)*exp(x)*exp(2*x)^14+56*x*exp(x)*exp(2*x)^12)*ln(x)+(33*x^2+2*x)*exp(x)*exp(2*x)^16+8*x*exp(x)*exp(2*x)^14)
*exp(1/3*(x^2*exp(x)*ln(x)^8+8*x^2*exp(x)*exp(2*x)^2*ln(x)^7+28*x^2*exp(x)*exp(2*x)^4*ln(x)^6+56*x^2*exp(x)*ex
p(2*x)^6*ln(x)^5+70*x^2*exp(x)*exp(2*x)^8*ln(x)^4+56*x^2*exp(x)*exp(2*x)^10*ln(x)^3+28*x^2*exp(x)*exp(2*x)^12*
ln(x)^2+8*x^2*exp(x)*exp(2*x)^14*ln(x)+x^2*exp(x)*exp(2*x)^16)/exp(4))/exp(4),x,method=_RETURNVERBOSE)

[Out]

exp(1/3*x^2*(exp(x)*ln(x)^8+8*ln(x)^7*exp(5*x)+28*ln(x)^6*exp(9*x)+56*ln(x)^5*exp(13*x)+70*ln(x)^4*exp(17*x)+5
6*ln(x)^3*exp(21*x)+28*ln(x)^2*exp(25*x)+8*ln(x)*exp(29*x)+exp(33*x))*exp(-4))

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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 129 vs. \(2 (19) = 38\).
time = 0.66, size = 129, normalized size = 5.38 \begin {gather*} e^{\left (\frac {1}{3} \, x^{2} e^{\left (x - 4\right )} \log \left (x\right )^{8} + \frac {8}{3} \, x^{2} e^{\left (5 \, x - 4\right )} \log \left (x\right )^{7} + \frac {28}{3} \, x^{2} e^{\left (9 \, x - 4\right )} \log \left (x\right )^{6} + \frac {56}{3} \, x^{2} e^{\left (13 \, x - 4\right )} \log \left (x\right )^{5} + \frac {70}{3} \, x^{2} e^{\left (17 \, x - 4\right )} \log \left (x\right )^{4} + \frac {56}{3} \, x^{2} e^{\left (21 \, x - 4\right )} \log \left (x\right )^{3} + \frac {28}{3} \, x^{2} e^{\left (25 \, x - 4\right )} \log \left (x\right )^{2} + \frac {8}{3} \, x^{2} e^{\left (29 \, x - 4\right )} \log \left (x\right ) + \frac {1}{3} \, x^{2} e^{\left (33 \, x - 4\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*((x^2+2*x)*exp(x)*log(x)^8+((40*x^2+16*x)*exp(x)*exp(2*x)^2+8*exp(x)*x)*log(x)^7+((252*x^2+56*x)
*exp(x)*exp(2*x)^4+56*x*exp(x)*exp(2*x)^2)*log(x)^6+((728*x^2+112*x)*exp(x)*exp(2*x)^6+168*x*exp(x)*exp(2*x)^4
)*log(x)^5+((1190*x^2+140*x)*exp(x)*exp(2*x)^8+280*x*exp(x)*exp(2*x)^6)*log(x)^4+((1176*x^2+112*x)*exp(x)*exp(
2*x)^10+280*x*exp(x)*exp(2*x)^8)*log(x)^3+((700*x^2+56*x)*exp(x)*exp(2*x)^12+168*x*exp(x)*exp(2*x)^10)*log(x)^
2+((232*x^2+16*x)*exp(x)*exp(2*x)^14+56*x*exp(x)*exp(2*x)^12)*log(x)+(33*x^2+2*x)*exp(x)*exp(2*x)^16+8*x*exp(x
)*exp(2*x)^14)*exp(1/3*(x^2*exp(x)*log(x)^8+8*x^2*exp(x)*exp(2*x)^2*log(x)^7+28*x^2*exp(x)*exp(2*x)^4*log(x)^6
+56*x^2*exp(x)*exp(2*x)^6*log(x)^5+70*x^2*exp(x)*exp(2*x)^8*log(x)^4+56*x^2*exp(x)*exp(2*x)^10*log(x)^3+28*x^2
*exp(x)*exp(2*x)^12*log(x)^2+8*x^2*exp(x)*exp(2*x)^14*log(x)+x^2*exp(x)*exp(2*x)^16)/exp(4))/exp(4),x, algorit
hm="maxima")

[Out]

e^(1/3*x^2*e^(x - 4)*log(x)^8 + 8/3*x^2*e^(5*x - 4)*log(x)^7 + 28/3*x^2*e^(9*x - 4)*log(x)^6 + 56/3*x^2*e^(13*
x - 4)*log(x)^5 + 70/3*x^2*e^(17*x - 4)*log(x)^4 + 56/3*x^2*e^(21*x - 4)*log(x)^3 + 28/3*x^2*e^(25*x - 4)*log(
x)^2 + 8/3*x^2*e^(29*x - 4)*log(x) + 1/3*x^2*e^(33*x - 4))

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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 119 vs. \(2 (19) = 38\).
time = 0.47, size = 119, normalized size = 4.96 \begin {gather*} e^{\left (\frac {1}{3} \, {\left (x^{2} e^{x} \log \left (x\right )^{8} + 8 \, x^{2} e^{\left (5 \, x\right )} \log \left (x\right )^{7} + 28 \, x^{2} e^{\left (9 \, x\right )} \log \left (x\right )^{6} + 56 \, x^{2} e^{\left (13 \, x\right )} \log \left (x\right )^{5} + 70 \, x^{2} e^{\left (17 \, x\right )} \log \left (x\right )^{4} + 56 \, x^{2} e^{\left (21 \, x\right )} \log \left (x\right )^{3} + 28 \, x^{2} e^{\left (25 \, x\right )} \log \left (x\right )^{2} + 8 \, x^{2} e^{\left (29 \, x\right )} \log \left (x\right ) + x^{2} e^{\left (33 \, x\right )} - 12 \, e^{4}\right )} e^{\left (-4\right )} + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*((x^2+2*x)*exp(x)*log(x)^8+((40*x^2+16*x)*exp(x)*exp(2*x)^2+8*exp(x)*x)*log(x)^7+((252*x^2+56*x)
*exp(x)*exp(2*x)^4+56*x*exp(x)*exp(2*x)^2)*log(x)^6+((728*x^2+112*x)*exp(x)*exp(2*x)^6+168*x*exp(x)*exp(2*x)^4
)*log(x)^5+((1190*x^2+140*x)*exp(x)*exp(2*x)^8+280*x*exp(x)*exp(2*x)^6)*log(x)^4+((1176*x^2+112*x)*exp(x)*exp(
2*x)^10+280*x*exp(x)*exp(2*x)^8)*log(x)^3+((700*x^2+56*x)*exp(x)*exp(2*x)^12+168*x*exp(x)*exp(2*x)^10)*log(x)^
2+((232*x^2+16*x)*exp(x)*exp(2*x)^14+56*x*exp(x)*exp(2*x)^12)*log(x)+(33*x^2+2*x)*exp(x)*exp(2*x)^16+8*x*exp(x
)*exp(2*x)^14)*exp(1/3*(x^2*exp(x)*log(x)^8+8*x^2*exp(x)*exp(2*x)^2*log(x)^7+28*x^2*exp(x)*exp(2*x)^4*log(x)^6
+56*x^2*exp(x)*exp(2*x)^6*log(x)^5+70*x^2*exp(x)*exp(2*x)^8*log(x)^4+56*x^2*exp(x)*exp(2*x)^10*log(x)^3+28*x^2
*exp(x)*exp(2*x)^12*log(x)^2+8*x^2*exp(x)*exp(2*x)^14*log(x)+x^2*exp(x)*exp(2*x)^16)/exp(4))/exp(4),x, algorit
hm="fricas")

[Out]

e^(1/3*(x^2*e^x*log(x)^8 + 8*x^2*e^(5*x)*log(x)^7 + 28*x^2*e^(9*x)*log(x)^6 + 56*x^2*e^(13*x)*log(x)^5 + 70*x^
2*e^(17*x)*log(x)^4 + 56*x^2*e^(21*x)*log(x)^3 + 28*x^2*e^(25*x)*log(x)^2 + 8*x^2*e^(29*x)*log(x) + x^2*e^(33*
x) - 12*e^4)*e^(-4) + 4)

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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 144 vs. \(2 (22) = 44\).
time = 1.99, size = 144, normalized size = 6.00 \begin {gather*} e^{\frac {\frac {x^{2} e^{33 x}}{3} + \frac {8 x^{2} e^{29 x} \log {\left (x \right )}}{3} + \frac {28 x^{2} e^{25 x} \log {\left (x \right )}^{2}}{3} + \frac {56 x^{2} e^{21 x} \log {\left (x \right )}^{3}}{3} + \frac {70 x^{2} e^{17 x} \log {\left (x \right )}^{4}}{3} + \frac {56 x^{2} e^{13 x} \log {\left (x \right )}^{5}}{3} + \frac {28 x^{2} e^{9 x} \log {\left (x \right )}^{6}}{3} + \frac {8 x^{2} e^{5 x} \log {\left (x \right )}^{7}}{3} + \frac {x^{2} e^{x} \log {\left (x \right )}^{8}}{3}}{e^{4}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*((x**2+2*x)*exp(x)*ln(x)**8+((40*x**2+16*x)*exp(x)*exp(2*x)**2+8*exp(x)*x)*ln(x)**7+((252*x**2+5
6*x)*exp(x)*exp(2*x)**4+56*x*exp(x)*exp(2*x)**2)*ln(x)**6+((728*x**2+112*x)*exp(x)*exp(2*x)**6+168*x*exp(x)*ex
p(2*x)**4)*ln(x)**5+((1190*x**2+140*x)*exp(x)*exp(2*x)**8+280*x*exp(x)*exp(2*x)**6)*ln(x)**4+((1176*x**2+112*x
)*exp(x)*exp(2*x)**10+280*x*exp(x)*exp(2*x)**8)*ln(x)**3+((700*x**2+56*x)*exp(x)*exp(2*x)**12+168*x*exp(x)*exp
(2*x)**10)*ln(x)**2+((232*x**2+16*x)*exp(x)*exp(2*x)**14+56*x*exp(x)*exp(2*x)**12)*ln(x)+(33*x**2+2*x)*exp(x)*
exp(2*x)**16+8*x*exp(x)*exp(2*x)**14)*exp(1/3*(x**2*exp(x)*ln(x)**8+8*x**2*exp(x)*exp(2*x)**2*ln(x)**7+28*x**2
*exp(x)*exp(2*x)**4*ln(x)**6+56*x**2*exp(x)*exp(2*x)**6*ln(x)**5+70*x**2*exp(x)*exp(2*x)**8*ln(x)**4+56*x**2*e
xp(x)*exp(2*x)**10*ln(x)**3+28*x**2*exp(x)*exp(2*x)**12*ln(x)**2+8*x**2*exp(x)*exp(2*x)**14*ln(x)+x**2*exp(x)*
exp(2*x)**16)/exp(4))/exp(4),x)

[Out]

exp((x**2*exp(33*x)/3 + 8*x**2*exp(29*x)*log(x)/3 + 28*x**2*exp(25*x)*log(x)**2/3 + 56*x**2*exp(21*x)*log(x)**
3/3 + 70*x**2*exp(17*x)*log(x)**4/3 + 56*x**2*exp(13*x)*log(x)**5/3 + 28*x**2*exp(9*x)*log(x)**6/3 + 8*x**2*ex
p(5*x)*log(x)**7/3 + x**2*exp(x)*log(x)**8/3)*exp(-4))

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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*((x^2+2*x)*exp(x)*log(x)^8+((40*x^2+16*x)*exp(x)*exp(2*x)^2+8*exp(x)*x)*log(x)^7+((252*x^2+56*x)
*exp(x)*exp(2*x)^4+56*x*exp(x)*exp(2*x)^2)*log(x)^6+((728*x^2+112*x)*exp(x)*exp(2*x)^6+168*x*exp(x)*exp(2*x)^4
)*log(x)^5+((1190*x^2+140*x)*exp(x)*exp(2*x)^8+280*x*exp(x)*exp(2*x)^6)*log(x)^4+((1176*x^2+112*x)*exp(x)*exp(
2*x)^10+280*x*exp(x)*exp(2*x)^8)*log(x)^3+((700*x^2+56*x)*exp(x)*exp(2*x)^12+168*x*exp(x)*exp(2*x)^10)*log(x)^
2+((232*x^2+16*x)*exp(x)*exp(2*x)^14+56*x*exp(x)*exp(2*x)^12)*log(x)+(33*x^2+2*x)*exp(x)*exp(2*x)^16+8*x*exp(x
)*exp(2*x)^14)*exp(1/3*(x^2*exp(x)*log(x)^8+8*x^2*exp(x)*exp(2*x)^2*log(x)^7+28*x^2*exp(x)*exp(2*x)^4*log(x)^6
+56*x^2*exp(x)*exp(2*x)^6*log(x)^5+70*x^2*exp(x)*exp(2*x)^8*log(x)^4+56*x^2*exp(x)*exp(2*x)^10*log(x)^3+28*x^2
*exp(x)*exp(2*x)^12*log(x)^2+8*x^2*exp(x)*exp(2*x)^14*log(x)+x^2*exp(x)*exp(2*x)^16)/exp(4))/exp(4),x, algorit
hm="giac")

[Out]

integrate(1/3*((x^2 + 2*x)*e^x*log(x)^8 + 8*((5*x^2 + 2*x)*e^(5*x) + x*e^x)*log(x)^7 + 28*((9*x^2 + 2*x)*e^(9*
x) + 2*x*e^(5*x))*log(x)^6 + 56*((13*x^2 + 2*x)*e^(13*x) + 3*x*e^(9*x))*log(x)^5 + 70*((17*x^2 + 2*x)*e^(17*x)
+ 4*x*e^(13*x))*log(x)^4 + 56*((21*x^2 + 2*x)*e^(21*x) + 5*x*e^(17*x))*log(x)^3 + 28*((25*x^2 + 2*x)*e^(25*x)
+ 6*x*e^(21*x))*log(x)^2 + (33*x^2 + 2*x)*e^(33*x) + 8*x*e^(29*x) + 8*((29*x^2 + 2*x)*e^(29*x) + 7*x*e^(25*x)
)*log(x))*e^(1/3*(x^2*e^x*log(x)^8 + 8*x^2*e^(5*x)*log(x)^7 + 28*x^2*e^(9*x)*log(x)^6 + 56*x^2*e^(13*x)*log(x)
^5 + 70*x^2*e^(17*x)*log(x)^4 + 56*x^2*e^(21*x)*log(x)^3 + 28*x^2*e^(25*x)*log(x)^2 + 8*x^2*e^(29*x)*log(x) +
x^2*e^(33*x))*e^(-4) - 4), x)

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Mupad [B]
time = 6.24, size = 137, normalized size = 5.71 \begin {gather*} {\mathrm {e}}^{\frac {8\,x^2\,{\mathrm {e}}^{29\,x}\,{\mathrm {e}}^{-4}\,\ln \left (x\right )}{3}}\,{\mathrm {e}}^{\frac {x^2\,{\mathrm {e}}^{-4}\,{\mathrm {e}}^x\,{\ln \left (x\right )}^8}{3}}\,{\mathrm {e}}^{\frac {x^2\,{\mathrm {e}}^{33\,x}\,{\mathrm {e}}^{-4}}{3}}\,{\mathrm {e}}^{\frac {8\,x^2\,{\mathrm {e}}^{5\,x}\,{\mathrm {e}}^{-4}\,{\ln \left (x\right )}^7}{3}}\,{\mathrm {e}}^{\frac {28\,x^2\,{\mathrm {e}}^{9\,x}\,{\mathrm {e}}^{-4}\,{\ln \left (x\right )}^6}{3}}\,{\mathrm {e}}^{\frac {28\,x^2\,{\mathrm {e}}^{25\,x}\,{\mathrm {e}}^{-4}\,{\ln \left (x\right )}^2}{3}}\,{\mathrm {e}}^{\frac {56\,x^2\,{\mathrm {e}}^{13\,x}\,{\mathrm {e}}^{-4}\,{\ln \left (x\right )}^5}{3}}\,{\mathrm {e}}^{\frac {56\,x^2\,{\mathrm {e}}^{21\,x}\,{\mathrm {e}}^{-4}\,{\ln \left (x\right )}^3}{3}}\,{\mathrm {e}}^{\frac {70\,x^2\,{\mathrm {e}}^{17\,x}\,{\mathrm {e}}^{-4}\,{\ln \left (x\right )}^4}{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(-4)*exp(exp(-4)*((x^2*exp(33*x))/3 + (8*x^2*exp(29*x)*log(x))/3 + (x^2*exp(x)*log(x)^8)/3 + (8*x^2*ex
p(5*x)*log(x)^7)/3 + (28*x^2*exp(9*x)*log(x)^6)/3 + (56*x^2*exp(13*x)*log(x)^5)/3 + (70*x^2*exp(17*x)*log(x)^4
)/3 + (56*x^2*exp(21*x)*log(x)^3)/3 + (28*x^2*exp(25*x)*log(x)^2)/3))*(exp(33*x)*(2*x + 33*x^2) + 8*x*exp(29*x
) + log(x)^6*(exp(9*x)*(56*x + 252*x^2) + 56*x*exp(5*x)) + log(x)^2*(exp(25*x)*(56*x + 700*x^2) + 168*x*exp(21
*x)) + log(x)^5*(exp(13*x)*(112*x + 728*x^2) + 168*x*exp(9*x)) + log(x)^3*(exp(21*x)*(112*x + 1176*x^2) + 280*
x*exp(17*x)) + log(x)^4*(exp(17*x)*(140*x + 1190*x^2) + 280*x*exp(13*x)) + log(x)*(exp(29*x)*(16*x + 232*x^2)
+ 56*x*exp(25*x)) + log(x)^7*(exp(5*x)*(16*x + 40*x^2) + 8*x*exp(x)) + exp(x)*log(x)^8*(2*x + x^2)))/3,x)

[Out]

exp((8*x^2*exp(29*x)*exp(-4)*log(x))/3)*exp((x^2*exp(-4)*exp(x)*log(x)^8)/3)*exp((x^2*exp(33*x)*exp(-4))/3)*ex
p((8*x^2*exp(5*x)*exp(-4)*log(x)^7)/3)*exp((28*x^2*exp(9*x)*exp(-4)*log(x)^6)/3)*exp((28*x^2*exp(25*x)*exp(-4)
*log(x)^2)/3)*exp((56*x^2*exp(13*x)*exp(-4)*log(x)^5)/3)*exp((56*x^2*exp(21*x)*exp(-4)*log(x)^3)/3)*exp((70*x^
2*exp(17*x)*exp(-4)*log(x)^4)/3)

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