3.81.51 \(\int e^{e^{32}+e^{4 x^2}+x^8+4 x^9+6 x^{10}+4 x^{11}+x^{12}+e^{16} (-2 x^4-4 x^5-2 x^6)+e^{2 x^2} (2 e^{16}-2 x^4-4 x^5-2 x^6)+(4 x^7+16 x^8+24 x^9+16 x^{10}+4 x^{11}+e^{16} (-4 x^3-8 x^4-4 x^5)+e^{2 x^2} (-4 x^3-8 x^4-4 x^5)) \log (x)+(6 x^6+24 x^7+36 x^8+24 x^9+6 x^{10}+e^{16} (-2 x^2-4 x^3-2 x^4)+e^{2 x^2} (-2 x^2-4 x^3-2 x^4)) \log ^2(x)+(4 x^5+16 x^6+24 x^7+16 x^8+4 x^9) \log ^3(x)+(x^4+4 x^5+6 x^6+4 x^7+x^8) \log ^4(x)} (8 e^{4 x^2} x+4 x^6+24 x^7+60 x^8+76 x^9+48 x^{10}+12 x^{11}+e^{16} (-4 x^2-16 x^3-24 x^4-12 x^5)+e^{2 x^2} (8 e^{16} x-4 x^2-16 x^3-24 x^4-20 x^5-16 x^6-8 x^7)+(12 x^5+76 x^6+200 x^7+264 x^8+172 x^9+44 x^{10}+e^{16} (-4 x-20 x^2-36 x^3-20 x^4)+e^{2 x^2} (-4 x-20 x^2-36 x^3-36 x^4-32 x^5-16 x^6)) \log (x)+(12 x^4+84 x^5+240 x^6+336 x^7+228 x^8+60 x^9+e^{16} (-4 x-12 x^2-8 x^3)+e^{2 x^2} (-4 x-12 x^2-16 x^3-16 x^4-8 x^5)) \log ^2(x)+(4 x^3+36 x^4+120 x^5+184 x^6+132 x^7+36 x^8) \log ^3(x)+(4 x^3+20 x^4+36 x^5+28 x^6+8 x^7) \log ^4(x)) \, dx\) [8051]
Optimal. Leaf size=30 \[ e^{\left (e^{16}+e^{2 x^2}-\left (x+x^2\right )^2 (x+\log (x))^2\right )^2} \]
[Out]
exp((exp(x^2)^2+exp(16)-(x^2+x)^2*(x+ln(x))^2)^2)
________________________________________________________________________________________
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^(E^32 + E^(4*x^2) + x^8 + 4*x^9 + 6*x^10 + 4*x^11 + x^12 + E^16*(-2*x^4 - 4*x^5 - 2*x^6) + E^(2*x^2)*(2*
E^16 - 2*x^4 - 4*x^5 - 2*x^6) + (4*x^7 + 16*x^8 + 24*x^9 + 16*x^10 + 4*x^11 + E^16*(-4*x^3 - 8*x^4 - 4*x^5) +
E^(2*x^2)*(-4*x^3 - 8*x^4 - 4*x^5))*Log[x] + (6*x^6 + 24*x^7 + 36*x^8 + 24*x^9 + 6*x^10 + E^16*(-2*x^2 - 4*x^3
- 2*x^4) + E^(2*x^2)*(-2*x^2 - 4*x^3 - 2*x^4))*Log[x]^2 + (4*x^5 + 16*x^6 + 24*x^7 + 16*x^8 + 4*x^9)*Log[x]^3
+ (x^4 + 4*x^5 + 6*x^6 + 4*x^7 + x^8)*Log[x]^4)*(8*E^(4*x^2)*x + 4*x^6 + 24*x^7 + 60*x^8 + 76*x^9 + 48*x^10 +
12*x^11 + E^16*(-4*x^2 - 16*x^3 - 24*x^4 - 12*x^5) + E^(2*x^2)*(8*E^16*x - 4*x^2 - 16*x^3 - 24*x^4 - 20*x^5 -
16*x^6 - 8*x^7) + (12*x^5 + 76*x^6 + 200*x^7 + 264*x^8 + 172*x^9 + 44*x^10 + E^16*(-4*x - 20*x^2 - 36*x^3 - 2
0*x^4) + E^(2*x^2)*(-4*x - 20*x^2 - 36*x^3 - 36*x^4 - 32*x^5 - 16*x^6))*Log[x] + (12*x^4 + 84*x^5 + 240*x^6 +
336*x^7 + 228*x^8 + 60*x^9 + E^16*(-4*x - 12*x^2 - 8*x^3) + E^(2*x^2)*(-4*x - 12*x^2 - 16*x^3 - 16*x^4 - 8*x^5
))*Log[x]^2 + (4*x^3 + 36*x^4 + 120*x^5 + 184*x^6 + 132*x^7 + 36*x^8)*Log[x]^3 + (4*x^3 + 20*x^4 + 36*x^5 + 28
*x^6 + 8*x^7)*Log[x]^4),x]
[Out]
$Aborted
Rubi steps
Aborted
________________________________________________________________________________________
Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(184\) vs. \(2(30)=60\).
time = 1.75, size = 184, normalized size = 6.13 \begin {gather*} e^{e^{32}+e^{4 x^2}-2 e^{16} x^4-4 e^{16} x^5-2 e^{16} x^6+x^8+4 x^9+6 x^{10}+4 x^{11}+x^{12}+2 e^{2 x^2} \left (e^{16}-x^4 (1+x)^2\right )+2 x^2 (1+x)^2 \left (-e^{16}-e^{2 x^2}+3 x^4 (1+x)^2\right ) \log ^2(x)+4 x^5 (1+x)^4 \log ^3(x)+x^4 (1+x)^4 \log ^4(x)} x^{4 x^3 (1+x)^2 \left (-e^{16}-e^{2 x^2}+x^4 (1+x)^2\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[E^(E^32 + E^(4*x^2) + x^8 + 4*x^9 + 6*x^10 + 4*x^11 + x^12 + E^16*(-2*x^4 - 4*x^5 - 2*x^6) + E^(2*x^
2)*(2*E^16 - 2*x^4 - 4*x^5 - 2*x^6) + (4*x^7 + 16*x^8 + 24*x^9 + 16*x^10 + 4*x^11 + E^16*(-4*x^3 - 8*x^4 - 4*x
^5) + E^(2*x^2)*(-4*x^3 - 8*x^4 - 4*x^5))*Log[x] + (6*x^6 + 24*x^7 + 36*x^8 + 24*x^9 + 6*x^10 + E^16*(-2*x^2 -
4*x^3 - 2*x^4) + E^(2*x^2)*(-2*x^2 - 4*x^3 - 2*x^4))*Log[x]^2 + (4*x^5 + 16*x^6 + 24*x^7 + 16*x^8 + 4*x^9)*Lo
g[x]^3 + (x^4 + 4*x^5 + 6*x^6 + 4*x^7 + x^8)*Log[x]^4)*(8*E^(4*x^2)*x + 4*x^6 + 24*x^7 + 60*x^8 + 76*x^9 + 48*
x^10 + 12*x^11 + E^16*(-4*x^2 - 16*x^3 - 24*x^4 - 12*x^5) + E^(2*x^2)*(8*E^16*x - 4*x^2 - 16*x^3 - 24*x^4 - 20
*x^5 - 16*x^6 - 8*x^7) + (12*x^5 + 76*x^6 + 200*x^7 + 264*x^8 + 172*x^9 + 44*x^10 + E^16*(-4*x - 20*x^2 - 36*x
^3 - 20*x^4) + E^(2*x^2)*(-4*x - 20*x^2 - 36*x^3 - 36*x^4 - 32*x^5 - 16*x^6))*Log[x] + (12*x^4 + 84*x^5 + 240*
x^6 + 336*x^7 + 228*x^8 + 60*x^9 + E^16*(-4*x - 12*x^2 - 8*x^3) + E^(2*x^2)*(-4*x - 12*x^2 - 16*x^3 - 16*x^4 -
8*x^5))*Log[x]^2 + (4*x^3 + 36*x^4 + 120*x^5 + 184*x^6 + 132*x^7 + 36*x^8)*Log[x]^3 + (4*x^3 + 20*x^4 + 36*x^
5 + 28*x^6 + 8*x^7)*Log[x]^4),x]
[Out]
E^(E^32 + E^(4*x^2) - 2*E^16*x^4 - 4*E^16*x^5 - 2*E^16*x^6 + x^8 + 4*x^9 + 6*x^10 + 4*x^11 + x^12 + 2*E^(2*x^2
)*(E^16 - x^4*(1 + x)^2) + 2*x^2*(1 + x)^2*(-E^16 - E^(2*x^2) + 3*x^4*(1 + x)^2)*Log[x]^2 + 4*x^5*(1 + x)^4*Lo
g[x]^3 + x^4*(1 + x)^4*Log[x]^4)*x^(4*x^3*(1 + x)^2*(-E^16 - E^(2*x^2) + x^4*(1 + x)^2))
________________________________________________________________________________________
Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(343\) vs.
\(2(27)=54\).
time = 0.70, size = 344, normalized size = 11.47
| | |
| method |
result |
size |
| | |
| risch |
\(x^{-4 \left (-x^{6}-2 x^{5}-x^{4}+{\mathrm e}^{2 x^{2}}+{\mathrm e}^{16}\right ) \left (x +1\right )^{2} x^{3}} {\mathrm e}^{6 x^{6} \ln \left (x \right )^{4}+4 x^{7} \ln \left (x \right )^{4}+24 x^{7} \ln \left (x \right )^{3}+4 x^{9} \ln \left (x \right )^{3}+6 x^{10} \ln \left (x \right )^{2}+24 x^{7} \ln \left (x \right )^{2}+36 x^{8} \ln \left (x \right )^{2}+6 x^{6} \ln \left (x \right )^{2}+16 x^{8} \ln \left (x \right )^{3}+24 x^{9} \ln \left (x \right )^{2}+16 x^{6} \ln \left (x \right )^{3}+4 x^{5} \ln \left (x \right )^{3}+4 x^{5} \ln \left (x \right )^{4}+{\mathrm e}^{32}-2 x^{4} {\mathrm e}^{16}+x^{8} \ln \left (x \right )^{4}+x^{4} \ln \left (x \right )^{4}+{\mathrm e}^{4 x^{2}}+4 x^{11}+x^{12}+x^{8}+6 x^{10}+4 x^{9}-2 \ln \left (x \right )^{2} {\mathrm e}^{16} x^{4}-4 \ln \left (x \right )^{2} {\mathrm e}^{16} x^{3}-2 \ln \left (x \right )^{2} {\mathrm e}^{16} x^{2}-2 \ln \left (x \right )^{2} {\mathrm e}^{2 x^{2}} x^{4}-4 \ln \left (x \right )^{2} {\mathrm e}^{2 x^{2}} x^{3}-2 \ln \left (x \right )^{2} {\mathrm e}^{2 x^{2}} x^{2}+2 \,{\mathrm e}^{2 x^{2}+16}-2 \,{\mathrm e}^{2 x^{2}} x^{6}-4 \,{\mathrm e}^{2 x^{2}} x^{5}-2 \,{\mathrm e}^{2 x^{2}} x^{4}-2 \,{\mathrm e}^{16} x^{6}-4 \,{\mathrm e}^{16} x^{5}}\) |
\(344\) |
| | |
|
|
|
|
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((8*x^7+28*x^6+36*x^5+20*x^4+4*x^3)*ln(x)^4+(36*x^8+132*x^7+184*x^6+120*x^5+36*x^4+4*x^3)*ln(x)^3+((-8*x^5
-16*x^4-16*x^3-12*x^2-4*x)*exp(x^2)^2+(-8*x^3-12*x^2-4*x)*exp(16)+60*x^9+228*x^8+336*x^7+240*x^6+84*x^5+12*x^4
)*ln(x)^2+((-16*x^6-32*x^5-36*x^4-36*x^3-20*x^2-4*x)*exp(x^2)^2+(-20*x^4-36*x^3-20*x^2-4*x)*exp(16)+44*x^10+17
2*x^9+264*x^8+200*x^7+76*x^6+12*x^5)*ln(x)+8*x*exp(x^2)^4+(8*x*exp(16)-8*x^7-16*x^6-20*x^5-24*x^4-16*x^3-4*x^2
)*exp(x^2)^2+(-12*x^5-24*x^4-16*x^3-4*x^2)*exp(16)+12*x^11+48*x^10+76*x^9+60*x^8+24*x^7+4*x^6)*exp((x^8+4*x^7+
6*x^6+4*x^5+x^4)*ln(x)^4+(4*x^9+16*x^8+24*x^7+16*x^6+4*x^5)*ln(x)^3+((-2*x^4-4*x^3-2*x^2)*exp(x^2)^2+(-2*x^4-4
*x^3-2*x^2)*exp(16)+6*x^10+24*x^9+36*x^8+24*x^7+6*x^6)*ln(x)^2+((-4*x^5-8*x^4-4*x^3)*exp(x^2)^2+(-4*x^5-8*x^4-
4*x^3)*exp(16)+4*x^11+16*x^10+24*x^9+16*x^8+4*x^7)*ln(x)+exp(x^2)^4+(2*exp(16)-2*x^6-4*x^5-2*x^4)*exp(x^2)^2+e
xp(16)^2+(-2*x^6-4*x^5-2*x^4)*exp(16)+x^12+4*x^11+6*x^10+4*x^9+x^8),x,method=_RETURNVERBOSE)
[Out]
x^(-4*(-x^6-2*x^5-x^4+exp(2*x^2)+exp(16))*(x+1)^2*x^3)*exp(6*x^6*ln(x)^4+4*x^7*ln(x)^4+24*x^7*ln(x)^3+4*x^9*ln
(x)^3+6*x^10*ln(x)^2+24*x^7*ln(x)^2+36*x^8*ln(x)^2+6*x^6*ln(x)^2+16*x^8*ln(x)^3+24*x^9*ln(x)^2+16*x^6*ln(x)^3+
4*x^5*ln(x)^3+4*x^5*ln(x)^4+exp(32)-2*x^4*exp(16)+x^8*ln(x)^4+x^4*ln(x)^4+exp(4*x^2)+4*x^11+x^12+x^8+6*x^10+4*
x^9-2*ln(x)^2*exp(16)*x^4-4*ln(x)^2*exp(16)*x^3-2*ln(x)^2*exp(16)*x^2-2*ln(x)^2*exp(2*x^2)*x^4-4*ln(x)^2*exp(2
*x^2)*x^3-2*ln(x)^2*exp(2*x^2)*x^2+2*exp(2*x^2+16)-2*exp(2*x^2)*x^6-4*exp(2*x^2)*x^5-2*exp(2*x^2)*x^4-2*exp(16
)*x^6-4*exp(16)*x^5)
________________________________________________________________________________________
Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 407 vs.
\(2 (30) = 60\).
time = 1.82, size = 407, normalized size = 13.57 \begin {gather*} e^{\left (x^{12} + 4 \, x^{11} \log \left (x\right ) + 6 \, x^{10} \log \left (x\right )^{2} + 4 \, x^{9} \log \left (x\right )^{3} + x^{8} \log \left (x\right )^{4} + 4 \, x^{11} + 16 \, x^{10} \log \left (x\right ) + 24 \, x^{9} \log \left (x\right )^{2} + 16 \, x^{8} \log \left (x\right )^{3} + 4 \, x^{7} \log \left (x\right )^{4} + 6 \, x^{10} + 24 \, x^{9} \log \left (x\right ) + 36 \, x^{8} \log \left (x\right )^{2} + 24 \, x^{7} \log \left (x\right )^{3} + 6 \, x^{6} \log \left (x\right )^{4} + 4 \, x^{9} + 16 \, x^{8} \log \left (x\right ) + 24 \, x^{7} \log \left (x\right )^{2} + 16 \, x^{6} \log \left (x\right )^{3} + 4 \, x^{5} \log \left (x\right )^{4} + x^{8} + 4 \, x^{7} \log \left (x\right ) + 6 \, x^{6} \log \left (x\right )^{2} + 4 \, x^{5} \log \left (x\right )^{3} + x^{4} \log \left (x\right )^{4} - 2 \, x^{6} e^{16} - 2 \, x^{6} e^{\left (2 \, x^{2}\right )} - 4 \, x^{5} e^{16} \log \left (x\right ) - 4 \, x^{5} e^{\left (2 \, x^{2}\right )} \log \left (x\right ) - 2 \, x^{4} e^{16} \log \left (x\right )^{2} - 2 \, x^{4} e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{2} - 4 \, x^{5} e^{16} - 4 \, x^{5} e^{\left (2 \, x^{2}\right )} - 8 \, x^{4} e^{16} \log \left (x\right ) - 8 \, x^{4} e^{\left (2 \, x^{2}\right )} \log \left (x\right ) - 4 \, x^{3} e^{16} \log \left (x\right )^{2} - 4 \, x^{3} e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{2} - 2 \, x^{4} e^{16} - 2 \, x^{4} e^{\left (2 \, x^{2}\right )} - 4 \, x^{3} e^{16} \log \left (x\right ) - 4 \, x^{3} e^{\left (2 \, x^{2}\right )} \log \left (x\right ) - 2 \, x^{2} e^{16} \log \left (x\right )^{2} - 2 \, x^{2} e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{2} + e^{32} + e^{\left (4 \, x^{2}\right )} + 2 \, e^{\left (2 \, x^{2} + 16\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((8*x^7+28*x^6+36*x^5+20*x^4+4*x^3)*log(x)^4+(36*x^8+132*x^7+184*x^6+120*x^5+36*x^4+4*x^3)*log(x)^3+
((-8*x^5-16*x^4-16*x^3-12*x^2-4*x)*exp(x^2)^2+(-8*x^3-12*x^2-4*x)*exp(16)+60*x^9+228*x^8+336*x^7+240*x^6+84*x^
5+12*x^4)*log(x)^2+((-16*x^6-32*x^5-36*x^4-36*x^3-20*x^2-4*x)*exp(x^2)^2+(-20*x^4-36*x^3-20*x^2-4*x)*exp(16)+4
4*x^10+172*x^9+264*x^8+200*x^7+76*x^6+12*x^5)*log(x)+8*x*exp(x^2)^4+(8*x*exp(16)-8*x^7-16*x^6-20*x^5-24*x^4-16
*x^3-4*x^2)*exp(x^2)^2+(-12*x^5-24*x^4-16*x^3-4*x^2)*exp(16)+12*x^11+48*x^10+76*x^9+60*x^8+24*x^7+4*x^6)*exp((
x^8+4*x^7+6*x^6+4*x^5+x^4)*log(x)^4+(4*x^9+16*x^8+24*x^7+16*x^6+4*x^5)*log(x)^3+((-2*x^4-4*x^3-2*x^2)*exp(x^2)
^2+(-2*x^4-4*x^3-2*x^2)*exp(16)+6*x^10+24*x^9+36*x^8+24*x^7+6*x^6)*log(x)^2+((-4*x^5-8*x^4-4*x^3)*exp(x^2)^2+(
-4*x^5-8*x^4-4*x^3)*exp(16)+4*x^11+16*x^10+24*x^9+16*x^8+4*x^7)*log(x)+exp(x^2)^4+(2*exp(16)-2*x^6-4*x^5-2*x^4
)*exp(x^2)^2+exp(16)^2+(-2*x^6-4*x^5-2*x^4)*exp(16)+x^12+4*x^11+6*x^10+4*x^9+x^8),x, algorithm="maxima")
[Out]
e^(x^12 + 4*x^11*log(x) + 6*x^10*log(x)^2 + 4*x^9*log(x)^3 + x^8*log(x)^4 + 4*x^11 + 16*x^10*log(x) + 24*x^9*l
og(x)^2 + 16*x^8*log(x)^3 + 4*x^7*log(x)^4 + 6*x^10 + 24*x^9*log(x) + 36*x^8*log(x)^2 + 24*x^7*log(x)^3 + 6*x^
6*log(x)^4 + 4*x^9 + 16*x^8*log(x) + 24*x^7*log(x)^2 + 16*x^6*log(x)^3 + 4*x^5*log(x)^4 + x^8 + 4*x^7*log(x) +
6*x^6*log(x)^2 + 4*x^5*log(x)^3 + x^4*log(x)^4 - 2*x^6*e^16 - 2*x^6*e^(2*x^2) - 4*x^5*e^16*log(x) - 4*x^5*e^(
2*x^2)*log(x) - 2*x^4*e^16*log(x)^2 - 2*x^4*e^(2*x^2)*log(x)^2 - 4*x^5*e^16 - 4*x^5*e^(2*x^2) - 8*x^4*e^16*log
(x) - 8*x^4*e^(2*x^2)*log(x) - 4*x^3*e^16*log(x)^2 - 4*x^3*e^(2*x^2)*log(x)^2 - 2*x^4*e^16 - 2*x^4*e^(2*x^2) -
4*x^3*e^16*log(x) - 4*x^3*e^(2*x^2)*log(x) - 2*x^2*e^16*log(x)^2 - 2*x^2*e^(2*x^2)*log(x)^2 + e^32 + e^(4*x^2
) + 2*e^(2*x^2 + 16))
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 256 vs.
\(2 (30) = 60\).
time = 0.41, size = 256, normalized size = 8.53 \begin {gather*} e^{\left (x^{12} + 4 \, x^{11} + 6 \, x^{10} + 4 \, x^{9} + x^{8} + {\left (x^{8} + 4 \, x^{7} + 6 \, x^{6} + 4 \, x^{5} + x^{4}\right )} \log \left (x\right )^{4} + 4 \, {\left (x^{9} + 4 \, x^{8} + 6 \, x^{7} + 4 \, x^{6} + x^{5}\right )} \log \left (x\right )^{3} + 2 \, {\left (3 \, x^{10} + 12 \, x^{9} + 18 \, x^{8} + 12 \, x^{7} + 3 \, x^{6} - {\left (x^{4} + 2 \, x^{3} + x^{2}\right )} e^{16} - {\left (x^{4} + 2 \, x^{3} + x^{2}\right )} e^{\left (2 \, x^{2}\right )}\right )} \log \left (x\right )^{2} - 2 \, {\left (x^{6} + 2 \, x^{5} + x^{4}\right )} e^{16} - 2 \, {\left (x^{6} + 2 \, x^{5} + x^{4} - e^{16}\right )} e^{\left (2 \, x^{2}\right )} + 4 \, {\left (x^{11} + 4 \, x^{10} + 6 \, x^{9} + 4 \, x^{8} + x^{7} - {\left (x^{5} + 2 \, x^{4} + x^{3}\right )} e^{16} - {\left (x^{5} + 2 \, x^{4} + x^{3}\right )} e^{\left (2 \, x^{2}\right )}\right )} \log \left (x\right ) + e^{32} + e^{\left (4 \, x^{2}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((8*x^7+28*x^6+36*x^5+20*x^4+4*x^3)*log(x)^4+(36*x^8+132*x^7+184*x^6+120*x^5+36*x^4+4*x^3)*log(x)^3+
((-8*x^5-16*x^4-16*x^3-12*x^2-4*x)*exp(x^2)^2+(-8*x^3-12*x^2-4*x)*exp(16)+60*x^9+228*x^8+336*x^7+240*x^6+84*x^
5+12*x^4)*log(x)^2+((-16*x^6-32*x^5-36*x^4-36*x^3-20*x^2-4*x)*exp(x^2)^2+(-20*x^4-36*x^3-20*x^2-4*x)*exp(16)+4
4*x^10+172*x^9+264*x^8+200*x^7+76*x^6+12*x^5)*log(x)+8*x*exp(x^2)^4+(8*x*exp(16)-8*x^7-16*x^6-20*x^5-24*x^4-16
*x^3-4*x^2)*exp(x^2)^2+(-12*x^5-24*x^4-16*x^3-4*x^2)*exp(16)+12*x^11+48*x^10+76*x^9+60*x^8+24*x^7+4*x^6)*exp((
x^8+4*x^7+6*x^6+4*x^5+x^4)*log(x)^4+(4*x^9+16*x^8+24*x^7+16*x^6+4*x^5)*log(x)^3+((-2*x^4-4*x^3-2*x^2)*exp(x^2)
^2+(-2*x^4-4*x^3-2*x^2)*exp(16)+6*x^10+24*x^9+36*x^8+24*x^7+6*x^6)*log(x)^2+((-4*x^5-8*x^4-4*x^3)*exp(x^2)^2+(
-4*x^5-8*x^4-4*x^3)*exp(16)+4*x^11+16*x^10+24*x^9+16*x^8+4*x^7)*log(x)+exp(x^2)^4+(2*exp(16)-2*x^6-4*x^5-2*x^4
)*exp(x^2)^2+exp(16)^2+(-2*x^6-4*x^5-2*x^4)*exp(16)+x^12+4*x^11+6*x^10+4*x^9+x^8),x, algorithm="fricas")
[Out]
e^(x^12 + 4*x^11 + 6*x^10 + 4*x^9 + x^8 + (x^8 + 4*x^7 + 6*x^6 + 4*x^5 + x^4)*log(x)^4 + 4*(x^9 + 4*x^8 + 6*x^
7 + 4*x^6 + x^5)*log(x)^3 + 2*(3*x^10 + 12*x^9 + 18*x^8 + 12*x^7 + 3*x^6 - (x^4 + 2*x^3 + x^2)*e^16 - (x^4 + 2
*x^3 + x^2)*e^(2*x^2))*log(x)^2 - 2*(x^6 + 2*x^5 + x^4)*e^16 - 2*(x^6 + 2*x^5 + x^4 - e^16)*e^(2*x^2) + 4*(x^1
1 + 4*x^10 + 6*x^9 + 4*x^8 + x^7 - (x^5 + 2*x^4 + x^3)*e^16 - (x^5 + 2*x^4 + x^3)*e^(2*x^2))*log(x) + e^32 + e
^(4*x^2))
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 286 vs.
\(2 (26) = 52\).
time = 2.75, size = 286, normalized size = 9.53 \begin {gather*} e^{x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + x^{8} + \left (- 2 x^{6} - 4 x^{5} - 2 x^{4}\right ) e^{16} + \left (- 2 x^{6} - 4 x^{5} - 2 x^{4} + 2 e^{16}\right ) e^{2 x^{2}} + \left (x^{8} + 4 x^{7} + 6 x^{6} + 4 x^{5} + x^{4}\right ) \log {\left (x \right )}^{4} + \left (4 x^{9} + 16 x^{8} + 24 x^{7} + 16 x^{6} + 4 x^{5}\right ) \log {\left (x \right )}^{3} + \left (6 x^{10} + 24 x^{9} + 36 x^{8} + 24 x^{7} + 6 x^{6} + \left (- 2 x^{4} - 4 x^{3} - 2 x^{2}\right ) e^{2 x^{2}} + \left (- 2 x^{4} - 4 x^{3} - 2 x^{2}\right ) e^{16}\right ) \log {\left (x \right )}^{2} + \left (4 x^{11} + 16 x^{10} + 24 x^{9} + 16 x^{8} + 4 x^{7} + \left (- 4 x^{5} - 8 x^{4} - 4 x^{3}\right ) e^{2 x^{2}} + \left (- 4 x^{5} - 8 x^{4} - 4 x^{3}\right ) e^{16}\right ) \log {\left (x \right )} + e^{4 x^{2}} + e^{32}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((8*x**7+28*x**6+36*x**5+20*x**4+4*x**3)*ln(x)**4+(36*x**8+132*x**7+184*x**6+120*x**5+36*x**4+4*x**3
)*ln(x)**3+((-8*x**5-16*x**4-16*x**3-12*x**2-4*x)*exp(x**2)**2+(-8*x**3-12*x**2-4*x)*exp(16)+60*x**9+228*x**8+
336*x**7+240*x**6+84*x**5+12*x**4)*ln(x)**2+((-16*x**6-32*x**5-36*x**4-36*x**3-20*x**2-4*x)*exp(x**2)**2+(-20*
x**4-36*x**3-20*x**2-4*x)*exp(16)+44*x**10+172*x**9+264*x**8+200*x**7+76*x**6+12*x**5)*ln(x)+8*x*exp(x**2)**4+
(8*x*exp(16)-8*x**7-16*x**6-20*x**5-24*x**4-16*x**3-4*x**2)*exp(x**2)**2+(-12*x**5-24*x**4-16*x**3-4*x**2)*exp
(16)+12*x**11+48*x**10+76*x**9+60*x**8+24*x**7+4*x**6)*exp((x**8+4*x**7+6*x**6+4*x**5+x**4)*ln(x)**4+(4*x**9+1
6*x**8+24*x**7+16*x**6+4*x**5)*ln(x)**3+((-2*x**4-4*x**3-2*x**2)*exp(x**2)**2+(-2*x**4-4*x**3-2*x**2)*exp(16)+
6*x**10+24*x**9+36*x**8+24*x**7+6*x**6)*ln(x)**2+((-4*x**5-8*x**4-4*x**3)*exp(x**2)**2+(-4*x**5-8*x**4-4*x**3)
*exp(16)+4*x**11+16*x**10+24*x**9+16*x**8+4*x**7)*ln(x)+exp(x**2)**4+(2*exp(16)-2*x**6-4*x**5-2*x**4)*exp(x**2
)**2+exp(16)**2+(-2*x**6-4*x**5-2*x**4)*exp(16)+x**12+4*x**11+6*x**10+4*x**9+x**8),x)
[Out]
exp(x**12 + 4*x**11 + 6*x**10 + 4*x**9 + x**8 + (-2*x**6 - 4*x**5 - 2*x**4)*exp(16) + (-2*x**6 - 4*x**5 - 2*x*
*4 + 2*exp(16))*exp(2*x**2) + (x**8 + 4*x**7 + 6*x**6 + 4*x**5 + x**4)*log(x)**4 + (4*x**9 + 16*x**8 + 24*x**7
+ 16*x**6 + 4*x**5)*log(x)**3 + (6*x**10 + 24*x**9 + 36*x**8 + 24*x**7 + 6*x**6 + (-2*x**4 - 4*x**3 - 2*x**2)
*exp(2*x**2) + (-2*x**4 - 4*x**3 - 2*x**2)*exp(16))*log(x)**2 + (4*x**11 + 16*x**10 + 24*x**9 + 16*x**8 + 4*x*
*7 + (-4*x**5 - 8*x**4 - 4*x**3)*exp(2*x**2) + (-4*x**5 - 8*x**4 - 4*x**3)*exp(16))*log(x) + exp(4*x**2) + exp
(32))
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 407 vs.
\(2 (30) = 60\).
time = 6.41, size = 407, normalized size = 13.57 \begin {gather*} e^{\left (x^{12} + 4 \, x^{11} \log \left (x\right ) + 6 \, x^{10} \log \left (x\right )^{2} + 4 \, x^{9} \log \left (x\right )^{3} + x^{8} \log \left (x\right )^{4} + 4 \, x^{11} + 16 \, x^{10} \log \left (x\right ) + 24 \, x^{9} \log \left (x\right )^{2} + 16 \, x^{8} \log \left (x\right )^{3} + 4 \, x^{7} \log \left (x\right )^{4} + 6 \, x^{10} + 24 \, x^{9} \log \left (x\right ) + 36 \, x^{8} \log \left (x\right )^{2} + 24 \, x^{7} \log \left (x\right )^{3} + 6 \, x^{6} \log \left (x\right )^{4} + 4 \, x^{9} + 16 \, x^{8} \log \left (x\right ) + 24 \, x^{7} \log \left (x\right )^{2} + 16 \, x^{6} \log \left (x\right )^{3} + 4 \, x^{5} \log \left (x\right )^{4} + x^{8} + 4 \, x^{7} \log \left (x\right ) + 6 \, x^{6} \log \left (x\right )^{2} + 4 \, x^{5} \log \left (x\right )^{3} + x^{4} \log \left (x\right )^{4} - 2 \, x^{6} e^{16} - 2 \, x^{6} e^{\left (2 \, x^{2}\right )} - 4 \, x^{5} e^{16} \log \left (x\right ) - 4 \, x^{5} e^{\left (2 \, x^{2}\right )} \log \left (x\right ) - 2 \, x^{4} e^{16} \log \left (x\right )^{2} - 2 \, x^{4} e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{2} - 4 \, x^{5} e^{16} - 4 \, x^{5} e^{\left (2 \, x^{2}\right )} - 8 \, x^{4} e^{16} \log \left (x\right ) - 8 \, x^{4} e^{\left (2 \, x^{2}\right )} \log \left (x\right ) - 4 \, x^{3} e^{16} \log \left (x\right )^{2} - 4 \, x^{3} e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{2} - 2 \, x^{4} e^{16} - 2 \, x^{4} e^{\left (2 \, x^{2}\right )} - 4 \, x^{3} e^{16} \log \left (x\right ) - 4 \, x^{3} e^{\left (2 \, x^{2}\right )} \log \left (x\right ) - 2 \, x^{2} e^{16} \log \left (x\right )^{2} - 2 \, x^{2} e^{\left (2 \, x^{2}\right )} \log \left (x\right )^{2} + e^{32} + e^{\left (4 \, x^{2}\right )} + 2 \, e^{\left (2 \, x^{2} + 16\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(((8*x^7+28*x^6+36*x^5+20*x^4+4*x^3)*log(x)^4+(36*x^8+132*x^7+184*x^6+120*x^5+36*x^4+4*x^3)*log(x)^3+
((-8*x^5-16*x^4-16*x^3-12*x^2-4*x)*exp(x^2)^2+(-8*x^3-12*x^2-4*x)*exp(16)+60*x^9+228*x^8+336*x^7+240*x^6+84*x^
5+12*x^4)*log(x)^2+((-16*x^6-32*x^5-36*x^4-36*x^3-20*x^2-4*x)*exp(x^2)^2+(-20*x^4-36*x^3-20*x^2-4*x)*exp(16)+4
4*x^10+172*x^9+264*x^8+200*x^7+76*x^6+12*x^5)*log(x)+8*x*exp(x^2)^4+(8*x*exp(16)-8*x^7-16*x^6-20*x^5-24*x^4-16
*x^3-4*x^2)*exp(x^2)^2+(-12*x^5-24*x^4-16*x^3-4*x^2)*exp(16)+12*x^11+48*x^10+76*x^9+60*x^8+24*x^7+4*x^6)*exp((
x^8+4*x^7+6*x^6+4*x^5+x^4)*log(x)^4+(4*x^9+16*x^8+24*x^7+16*x^6+4*x^5)*log(x)^3+((-2*x^4-4*x^3-2*x^2)*exp(x^2)
^2+(-2*x^4-4*x^3-2*x^2)*exp(16)+6*x^10+24*x^9+36*x^8+24*x^7+6*x^6)*log(x)^2+((-4*x^5-8*x^4-4*x^3)*exp(x^2)^2+(
-4*x^5-8*x^4-4*x^3)*exp(16)+4*x^11+16*x^10+24*x^9+16*x^8+4*x^7)*log(x)+exp(x^2)^4+(2*exp(16)-2*x^6-4*x^5-2*x^4
)*exp(x^2)^2+exp(16)^2+(-2*x^6-4*x^5-2*x^4)*exp(16)+x^12+4*x^11+6*x^10+4*x^9+x^8),x, algorithm="giac")
[Out]
e^(x^12 + 4*x^11*log(x) + 6*x^10*log(x)^2 + 4*x^9*log(x)^3 + x^8*log(x)^4 + 4*x^11 + 16*x^10*log(x) + 24*x^9*l
og(x)^2 + 16*x^8*log(x)^3 + 4*x^7*log(x)^4 + 6*x^10 + 24*x^9*log(x) + 36*x^8*log(x)^2 + 24*x^7*log(x)^3 + 6*x^
6*log(x)^4 + 4*x^9 + 16*x^8*log(x) + 24*x^7*log(x)^2 + 16*x^6*log(x)^3 + 4*x^5*log(x)^4 + x^8 + 4*x^7*log(x) +
6*x^6*log(x)^2 + 4*x^5*log(x)^3 + x^4*log(x)^4 - 2*x^6*e^16 - 2*x^6*e^(2*x^2) - 4*x^5*e^16*log(x) - 4*x^5*e^(
2*x^2)*log(x) - 2*x^4*e^16*log(x)^2 - 2*x^4*e^(2*x^2)*log(x)^2 - 4*x^5*e^16 - 4*x^5*e^(2*x^2) - 8*x^4*e^16*log
(x) - 8*x^4*e^(2*x^2)*log(x) - 4*x^3*e^16*log(x)^2 - 4*x^3*e^(2*x^2)*log(x)^2 - 2*x^4*e^16 - 2*x^4*e^(2*x^2) -
4*x^3*e^16*log(x) - 4*x^3*e^(2*x^2)*log(x) - 2*x^2*e^16*log(x)^2 - 2*x^2*e^(2*x^2)*log(x)^2 + e^32 + e^(4*x^2
) + 2*e^(2*x^2 + 16))
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Mupad [B]
time = 7.67, size = 453, normalized size = 15.10 \begin {gather*} \frac {x^{4\,x^7}\,x^{4\,x^{11}}\,x^{16\,x^8}\,x^{16\,x^{10}}\,x^{24\,x^9}\,{\mathrm {e}}^{{\mathrm {e}}^{4\,x^2}}\,{\mathrm {e}}^{-2\,x^4\,{\mathrm {e}}^{16}}\,{\mathrm {e}}^{-2\,x^6\,{\mathrm {e}}^{16}}\,{\mathrm {e}}^{-4\,x^5\,{\mathrm {e}}^{16}}\,{\mathrm {e}}^{-2\,x^4\,{\mathrm {e}}^{2\,x^2}}\,{\mathrm {e}}^{-2\,x^6\,{\mathrm {e}}^{2\,x^2}}\,{\mathrm {e}}^{-4\,x^5\,{\mathrm {e}}^{2\,x^2}}\,{\mathrm {e}}^{x^8}\,{\mathrm {e}}^{x^{12}}\,{\mathrm {e}}^{-2\,x^2\,{\mathrm {e}}^{16}\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{-2\,x^4\,{\mathrm {e}}^{16}\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{-4\,x^3\,{\mathrm {e}}^{16}\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{-2\,x^2\,{\mathrm {e}}^{2\,x^2}\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{-2\,x^4\,{\mathrm {e}}^{2\,x^2}\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{-4\,x^3\,{\mathrm {e}}^{2\,x^2}\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{4\,x^9}\,{\mathrm {e}}^{4\,x^{11}}\,{\mathrm {e}}^{6\,x^{10}}\,{\mathrm {e}}^{2\,{\mathrm {e}}^{16}\,{\mathrm {e}}^{2\,x^2}}\,{\mathrm {e}}^{{\mathrm {e}}^{32}}\,{\mathrm {e}}^{x^4\,{\ln \left (x\right )}^4}\,{\mathrm {e}}^{x^8\,{\ln \left (x\right )}^4}\,{\mathrm {e}}^{4\,x^5\,{\ln \left (x\right )}^3}\,{\mathrm {e}}^{4\,x^5\,{\ln \left (x\right )}^4}\,{\mathrm {e}}^{6\,x^6\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{4\,x^7\,{\ln \left (x\right )}^4}\,{\mathrm {e}}^{6\,x^6\,{\ln \left (x\right )}^4}\,{\mathrm {e}}^{4\,x^9\,{\ln \left (x\right )}^3}\,{\mathrm {e}}^{6\,x^{10}\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{16\,x^6\,{\ln \left (x\right )}^3}\,{\mathrm {e}}^{16\,x^8\,{\ln \left (x\right )}^3}\,{\mathrm {e}}^{24\,x^7\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{24\,x^7\,{\ln \left (x\right )}^3}\,{\mathrm {e}}^{24\,x^9\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{36\,x^8\,{\ln \left (x\right )}^2}}{x^{4\,x^3\,{\mathrm {e}}^{16}}\,x^{4\,x^5\,{\mathrm {e}}^{16}}\,x^{8\,x^4\,{\mathrm {e}}^{16}}\,x^{4\,x^3\,{\mathrm {e}}^{2\,x^2}}\,x^{4\,x^5\,{\mathrm {e}}^{2\,x^2}}\,x^{8\,x^4\,{\mathrm {e}}^{2\,x^2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(exp(exp(32) + exp(4*x^2) + log(x)^3*(4*x^5 + 16*x^6 + 24*x^7 + 16*x^8 + 4*x^9) + log(x)^4*(x^4 + 4*x^5 + 6
*x^6 + 4*x^7 + x^8) + log(x)*(4*x^7 - exp(16)*(4*x^3 + 8*x^4 + 4*x^5) + 16*x^8 + 24*x^9 + 16*x^10 + 4*x^11 - e
xp(2*x^2)*(4*x^3 + 8*x^4 + 4*x^5)) - exp(2*x^2)*(2*x^4 - 2*exp(16) + 4*x^5 + 2*x^6) - exp(16)*(2*x^4 + 4*x^5 +
2*x^6) + x^8 + 4*x^9 + 6*x^10 + 4*x^11 + x^12 + log(x)^2*(6*x^6 - exp(16)*(2*x^2 + 4*x^3 + 2*x^4) + 24*x^7 +
36*x^8 + 24*x^9 + 6*x^10 - exp(2*x^2)*(2*x^2 + 4*x^3 + 2*x^4)))*(log(x)^4*(4*x^3 + 20*x^4 + 36*x^5 + 28*x^6 +
8*x^7) + log(x)^3*(4*x^3 + 36*x^4 + 120*x^5 + 184*x^6 + 132*x^7 + 36*x^8) + 8*x*exp(4*x^2) + log(x)^2*(12*x^4
- exp(16)*(4*x + 12*x^2 + 8*x^3) - exp(2*x^2)*(4*x + 12*x^2 + 16*x^3 + 16*x^4 + 8*x^5) + 84*x^5 + 240*x^6 + 33
6*x^7 + 228*x^8 + 60*x^9) + log(x)*(12*x^5 - exp(16)*(4*x + 20*x^2 + 36*x^3 + 20*x^4) - exp(2*x^2)*(4*x + 20*x
^2 + 36*x^3 + 36*x^4 + 32*x^5 + 16*x^6) + 76*x^6 + 200*x^7 + 264*x^8 + 172*x^9 + 44*x^10) + 4*x^6 + 24*x^7 + 6
0*x^8 + 76*x^9 + 48*x^10 + 12*x^11 - exp(2*x^2)*(4*x^2 - 8*x*exp(16) + 16*x^3 + 24*x^4 + 20*x^5 + 16*x^6 + 8*x
^7) - exp(16)*(4*x^2 + 16*x^3 + 24*x^4 + 12*x^5)),x)
[Out]
(x^(4*x^7)*x^(4*x^11)*x^(16*x^8)*x^(16*x^10)*x^(24*x^9)*exp(exp(4*x^2))*exp(-2*x^4*exp(16))*exp(-2*x^6*exp(16)
)*exp(-4*x^5*exp(16))*exp(-2*x^4*exp(2*x^2))*exp(-2*x^6*exp(2*x^2))*exp(-4*x^5*exp(2*x^2))*exp(x^8)*exp(x^12)*
exp(-2*x^2*exp(16)*log(x)^2)*exp(-2*x^4*exp(16)*log(x)^2)*exp(-4*x^3*exp(16)*log(x)^2)*exp(-2*x^2*exp(2*x^2)*l
og(x)^2)*exp(-2*x^4*exp(2*x^2)*log(x)^2)*exp(-4*x^3*exp(2*x^2)*log(x)^2)*exp(4*x^9)*exp(4*x^11)*exp(6*x^10)*ex
p(2*exp(16)*exp(2*x^2))*exp(exp(32))*exp(x^4*log(x)^4)*exp(x^8*log(x)^4)*exp(4*x^5*log(x)^3)*exp(4*x^5*log(x)^
4)*exp(6*x^6*log(x)^2)*exp(4*x^7*log(x)^4)*exp(6*x^6*log(x)^4)*exp(4*x^9*log(x)^3)*exp(6*x^10*log(x)^2)*exp(16
*x^6*log(x)^3)*exp(16*x^8*log(x)^3)*exp(24*x^7*log(x)^2)*exp(24*x^7*log(x)^3)*exp(24*x^9*log(x)^2)*exp(36*x^8*
log(x)^2))/(x^(4*x^3*exp(16))*x^(4*x^5*exp(16))*x^(8*x^4*exp(16))*x^(4*x^3*exp(2*x^2))*x^(4*x^5*exp(2*x^2))*x^
(8*x^4*exp(2*x^2)))
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