3.80.98 \(\int \frac {-e^{5 x}-5 e^{4 x} x-10 e^{3 x} x^2-10 e^{2 x} x^3-5 e^x x^4-x^5+e^{\frac {1-4 x+2 x^2+8 x^3-5 x^4-9 x^5+2 x^6+4 x^7+x^8+e^{4 x} (1+3 x+6 x^2+4 x^3+x^4)+e^{3 x} (-4-8 x+20 x^3+16 x^4+4 x^5)+e^{2 x} (6-24 x^2-18 x^3+24 x^4+24 x^5+6 x^6)+e^x (-4+8 x+12 x^2-20 x^3-24 x^4+12 x^5+16 x^6+4 x^7)}{e^{4 x}+4 e^{3 x} x+6 e^{2 x} x^2+4 e^x x^3+x^4}} (-4 x^2+12 x^3-4 x^4-8 x^5+x^6-9 x^7+4 x^8+12 x^9+4 x^{10}+e^{5 x} (x+3 x^2+12 x^3+12 x^4+4 x^5)+e^{4 x} (-3 x^2+3 x^3+60 x^4+64 x^5+20 x^6)+e^{3 x} (4 x^2-26 x^3-30 x^4+112 x^5+132 x^6+40 x^7)+e^{2 x} (-4 x^2+12 x^3-38 x^4-66 x^5+96 x^6+132 x^7+40 x^8)+e^x (8 x^2-8 x^3-15 x^5-45 x^6+36 x^7+64 x^8+20 x^9))}{e^{5 x} x+5 e^{4 x} x^2+10 e^{3 x} x^3+10 e^{2 x} x^4+5 e^x x^5+x^6} \, dx\)
Optimal. Leaf size=27 \[ e^{-x+\left (1+x-\frac {1}{e^x+x}\right )^4} x-\log (x) \]
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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^(5*x) - 5*E^(4*x)*x - 10*E^(3*x)*x^2 - 10*E^(2*x)*x^3 - 5*E^x*x^4 - x^5 + E^((1 - 4*x + 2*x^2 + 8*x^3
- 5*x^4 - 9*x^5 + 2*x^6 + 4*x^7 + x^8 + E^(4*x)*(1 + 3*x + 6*x^2 + 4*x^3 + x^4) + E^(3*x)*(-4 - 8*x + 20*x^3 +
16*x^4 + 4*x^5) + E^(2*x)*(6 - 24*x^2 - 18*x^3 + 24*x^4 + 24*x^5 + 6*x^6) + E^x*(-4 + 8*x + 12*x^2 - 20*x^3 -
24*x^4 + 12*x^5 + 16*x^6 + 4*x^7))/(E^(4*x) + 4*E^(3*x)*x + 6*E^(2*x)*x^2 + 4*E^x*x^3 + x^4))*(-4*x^2 + 12*x^
3 - 4*x^4 - 8*x^5 + x^6 - 9*x^7 + 4*x^8 + 12*x^9 + 4*x^10 + E^(5*x)*(x + 3*x^2 + 12*x^3 + 12*x^4 + 4*x^5) + E^
(4*x)*(-3*x^2 + 3*x^3 + 60*x^4 + 64*x^5 + 20*x^6) + E^(3*x)*(4*x^2 - 26*x^3 - 30*x^4 + 112*x^5 + 132*x^6 + 40*
x^7) + E^(2*x)*(-4*x^2 + 12*x^3 - 38*x^4 - 66*x^5 + 96*x^6 + 132*x^7 + 40*x^8) + E^x*(8*x^2 - 8*x^3 - 15*x^5 -
45*x^6 + 36*x^7 + 64*x^8 + 20*x^9)))/(E^(5*x)*x + 5*E^(4*x)*x^2 + 10*E^(3*x)*x^3 + 10*E^(2*x)*x^4 + 5*E^x*x^5
+ x^6),x]
[Out]
$Aborted
Rubi steps
Aborted
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Mathematica [B] time = 8.16, size = 74, normalized size = 2.74 \begin {gather*} e^{1+3 x+6 x^2+4 x^3+x^4+\frac {1}{\left (e^x+x\right )^4}-\frac {4 (1+x)}{\left (e^x+x\right )^3}+\frac {6 (1+x)^2}{\left (e^x+x\right )^2}-\frac {4 (1+x)^3}{e^x+x}} x-\log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(-E^(5*x) - 5*E^(4*x)*x - 10*E^(3*x)*x^2 - 10*E^(2*x)*x^3 - 5*E^x*x^4 - x^5 + E^((1 - 4*x + 2*x^2 +
8*x^3 - 5*x^4 - 9*x^5 + 2*x^6 + 4*x^7 + x^8 + E^(4*x)*(1 + 3*x + 6*x^2 + 4*x^3 + x^4) + E^(3*x)*(-4 - 8*x + 20
*x^3 + 16*x^4 + 4*x^5) + E^(2*x)*(6 - 24*x^2 - 18*x^3 + 24*x^4 + 24*x^5 + 6*x^6) + E^x*(-4 + 8*x + 12*x^2 - 20
*x^3 - 24*x^4 + 12*x^5 + 16*x^6 + 4*x^7))/(E^(4*x) + 4*E^(3*x)*x + 6*E^(2*x)*x^2 + 4*E^x*x^3 + x^4))*(-4*x^2 +
12*x^3 - 4*x^4 - 8*x^5 + x^6 - 9*x^7 + 4*x^8 + 12*x^9 + 4*x^10 + E^(5*x)*(x + 3*x^2 + 12*x^3 + 12*x^4 + 4*x^5
) + E^(4*x)*(-3*x^2 + 3*x^3 + 60*x^4 + 64*x^5 + 20*x^6) + E^(3*x)*(4*x^2 - 26*x^3 - 30*x^4 + 112*x^5 + 132*x^6
+ 40*x^7) + E^(2*x)*(-4*x^2 + 12*x^3 - 38*x^4 - 66*x^5 + 96*x^6 + 132*x^7 + 40*x^8) + E^x*(8*x^2 - 8*x^3 - 15
*x^5 - 45*x^6 + 36*x^7 + 64*x^8 + 20*x^9)))/(E^(5*x)*x + 5*E^(4*x)*x^2 + 10*E^(3*x)*x^3 + 10*E^(2*x)*x^4 + 5*E
^x*x^5 + x^6),x]
[Out]
E^(1 + 3*x + 6*x^2 + 4*x^3 + x^4 + (E^x + x)^(-4) - (4*(1 + x))/(E^x + x)^3 + (6*(1 + x)^2)/(E^x + x)^2 - (4*(
1 + x)^3)/(E^x + x))*x - Log[x]
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fricas [B] time = 0.73, size = 195, normalized size = 7.22 \begin {gather*} x e^{\left (\frac {x^{8} + 4 \, x^{7} + 2 \, x^{6} - 9 \, x^{5} - 5 \, x^{4} + 8 \, x^{3} + 2 \, x^{2} + {\left (x^{4} + 4 \, x^{3} + 6 \, x^{2} + 3 \, x + 1\right )} e^{\left (4 \, x\right )} + 4 \, {\left (x^{5} + 4 \, x^{4} + 5 \, x^{3} - 2 \, x - 1\right )} e^{\left (3 \, x\right )} + 6 \, {\left (x^{6} + 4 \, x^{5} + 4 \, x^{4} - 3 \, x^{3} - 4 \, x^{2} + 1\right )} e^{\left (2 \, x\right )} + 4 \, {\left (x^{7} + 4 \, x^{6} + 3 \, x^{5} - 6 \, x^{4} - 5 \, x^{3} + 3 \, x^{2} + 2 \, x - 1\right )} e^{x} - 4 \, x + 1}{x^{4} + 4 \, x^{3} e^{x} + 6 \, x^{2} e^{\left (2 \, x\right )} + 4 \, x e^{\left (3 \, x\right )} + e^{\left (4 \, x\right )}}\right )} - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((4*x^5+12*x^4+12*x^3+3*x^2+x)*exp(x)^5+(20*x^6+64*x^5+60*x^4+3*x^3-3*x^2)*exp(x)^4+(40*x^7+132*x^6
+112*x^5-30*x^4-26*x^3+4*x^2)*exp(x)^3+(40*x^8+132*x^7+96*x^6-66*x^5-38*x^4+12*x^3-4*x^2)*exp(x)^2+(20*x^9+64*
x^8+36*x^7-45*x^6-15*x^5-8*x^3+8*x^2)*exp(x)+4*x^10+12*x^9+4*x^8-9*x^7+x^6-8*x^5-4*x^4+12*x^3-4*x^2)*exp(((x^4
+4*x^3+6*x^2+3*x+1)*exp(x)^4+(4*x^5+16*x^4+20*x^3-8*x-4)*exp(x)^3+(6*x^6+24*x^5+24*x^4-18*x^3-24*x^2+6)*exp(x)
^2+(4*x^7+16*x^6+12*x^5-24*x^4-20*x^3+12*x^2+8*x-4)*exp(x)+x^8+4*x^7+2*x^6-9*x^5-5*x^4+8*x^3+2*x^2-4*x+1)/(exp
(x)^4+4*x*exp(x)^3+6*exp(x)^2*x^2+4*exp(x)*x^3+x^4))-exp(x)^5-5*x*exp(x)^4-10*x^2*exp(x)^3-10*exp(x)^2*x^3-5*e
xp(x)*x^4-x^5)/(x*exp(x)^5+5*x^2*exp(x)^4+10*x^3*exp(x)^3+10*exp(x)^2*x^4+5*x^5*exp(x)+x^6),x, algorithm="fric
as")
[Out]
x*e^((x^8 + 4*x^7 + 2*x^6 - 9*x^5 - 5*x^4 + 8*x^3 + 2*x^2 + (x^4 + 4*x^3 + 6*x^2 + 3*x + 1)*e^(4*x) + 4*(x^5 +
4*x^4 + 5*x^3 - 2*x - 1)*e^(3*x) + 6*(x^6 + 4*x^5 + 4*x^4 - 3*x^3 - 4*x^2 + 1)*e^(2*x) + 4*(x^7 + 4*x^6 + 3*x
^5 - 6*x^4 - 5*x^3 + 3*x^2 + 2*x - 1)*e^x - 4*x + 1)/(x^4 + 4*x^3*e^x + 6*x^2*e^(2*x) + 4*x*e^(3*x) + e^(4*x))
) - log(x)
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giac [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((4*x^5+12*x^4+12*x^3+3*x^2+x)*exp(x)^5+(20*x^6+64*x^5+60*x^4+3*x^3-3*x^2)*exp(x)^4+(40*x^7+132*x^6
+112*x^5-30*x^4-26*x^3+4*x^2)*exp(x)^3+(40*x^8+132*x^7+96*x^6-66*x^5-38*x^4+12*x^3-4*x^2)*exp(x)^2+(20*x^9+64*
x^8+36*x^7-45*x^6-15*x^5-8*x^3+8*x^2)*exp(x)+4*x^10+12*x^9+4*x^8-9*x^7+x^6-8*x^5-4*x^4+12*x^3-4*x^2)*exp(((x^4
+4*x^3+6*x^2+3*x+1)*exp(x)^4+(4*x^5+16*x^4+20*x^3-8*x-4)*exp(x)^3+(6*x^6+24*x^5+24*x^4-18*x^3-24*x^2+6)*exp(x)
^2+(4*x^7+16*x^6+12*x^5-24*x^4-20*x^3+12*x^2+8*x-4)*exp(x)+x^8+4*x^7+2*x^6-9*x^5-5*x^4+8*x^3+2*x^2-4*x+1)/(exp
(x)^4+4*x*exp(x)^3+6*exp(x)^2*x^2+4*exp(x)*x^3+x^4))-exp(x)^5-5*x*exp(x)^4-10*x^2*exp(x)^3-10*exp(x)^2*x^3-5*e
xp(x)*x^4-x^5)/(x*exp(x)^5+5*x^2*exp(x)^4+10*x^3*exp(x)^3+10*exp(x)^2*x^4+5*x^5*exp(x)+x^6),x, algorithm="giac
")
[Out]
Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,sageVARx):;OUTP
UT:Evaluation time: 6.45Unable to divide, perhaps due to rounding error%%%{-167772160,[4,36]%%%}+%%%{469762048
0,[4,35]%%%
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maple [B] time = 1.94, size = 260, normalized size = 9.63
|
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| method |
result |
size |
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| risch |
\(-\ln \relax (x )+x \,{\mathrm e}^{\frac {1-4 x +20 x^{3} {\mathrm e}^{3 x}+{\mathrm e}^{4 x}+4 x^{7} {\mathrm e}^{x}+12 x^{5} {\mathrm e}^{x}-4 \,{\mathrm e}^{3 x}+6 \,{\mathrm e}^{2 x}+4 x^{7}+x^{8}+2 x^{6}-9 x^{5}-5 x^{4}+8 x^{3}+2 x^{2}-4 \,{\mathrm e}^{x}-18 \,{\mathrm e}^{2 x} x^{3}+4 x^{3} {\mathrm e}^{4 x}+24 x^{5} {\mathrm e}^{2 x}-8 x \,{\mathrm e}^{3 x}-24 \,{\mathrm e}^{2 x} x^{2}+16 x^{6} {\mathrm e}^{x}-24 \,{\mathrm e}^{x} x^{4}+12 \,{\mathrm e}^{x} x^{2}-20 \,{\mathrm e}^{x} x^{3}+8 \,{\mathrm e}^{x} x +3 x \,{\mathrm e}^{4 x}+6 x^{2} {\mathrm e}^{4 x}+24 \,{\mathrm e}^{2 x} x^{4}+16 \,{\mathrm e}^{3 x} x^{4}+6 \,{\mathrm e}^{2 x} x^{6}+4 \,{\mathrm e}^{3 x} x^{5}+{\mathrm e}^{4 x} x^{4}}{{\mathrm e}^{4 x}+4 x \,{\mathrm e}^{3 x}+6 \,{\mathrm e}^{2 x} x^{2}+4 \,{\mathrm e}^{x} x^{3}+x^{4}}}\) |
\(260\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int((((4*x^5+12*x^4+12*x^3+3*x^2+x)*exp(x)^5+(20*x^6+64*x^5+60*x^4+3*x^3-3*x^2)*exp(x)^4+(40*x^7+132*x^6+112*x
^5-30*x^4-26*x^3+4*x^2)*exp(x)^3+(40*x^8+132*x^7+96*x^6-66*x^5-38*x^4+12*x^3-4*x^2)*exp(x)^2+(20*x^9+64*x^8+36
*x^7-45*x^6-15*x^5-8*x^3+8*x^2)*exp(x)+4*x^10+12*x^9+4*x^8-9*x^7+x^6-8*x^5-4*x^4+12*x^3-4*x^2)*exp(((x^4+4*x^3
+6*x^2+3*x+1)*exp(x)^4+(4*x^5+16*x^4+20*x^3-8*x-4)*exp(x)^3+(6*x^6+24*x^5+24*x^4-18*x^3-24*x^2+6)*exp(x)^2+(4*
x^7+16*x^6+12*x^5-24*x^4-20*x^3+12*x^2+8*x-4)*exp(x)+x^8+4*x^7+2*x^6-9*x^5-5*x^4+8*x^3+2*x^2-4*x+1)/(exp(x)^4+
4*x*exp(x)^3+6*exp(x)^2*x^2+4*exp(x)*x^3+x^4))-exp(x)^5-5*x*exp(x)^4-10*x^2*exp(x)^3-10*exp(x)^2*x^3-5*exp(x)*
x^4-x^5)/(x*exp(x)^5+5*x^2*exp(x)^4+10*x^3*exp(x)^3+10*exp(x)^2*x^4+5*x^5*exp(x)+x^6),x,method=_RETURNVERBOSE)
[Out]
-ln(x)+x*exp((1-4*x+20*x^3*exp(3*x)+exp(4*x)+4*x^7*exp(x)+12*x^5*exp(x)-4*exp(3*x)+6*exp(2*x)+4*x^7+x^8+2*x^6-
9*x^5-5*x^4+8*x^3+2*x^2-4*exp(x)-18*exp(2*x)*x^3+4*x^3*exp(4*x)+24*x^5*exp(2*x)-8*x*exp(3*x)-24*exp(2*x)*x^2+1
6*x^6*exp(x)-24*exp(x)*x^4+12*exp(x)*x^2-20*exp(x)*x^3+8*exp(x)*x+3*x*exp(4*x)+6*x^2*exp(4*x)+24*exp(2*x)*x^4+
16*exp(3*x)*x^4+6*exp(2*x)*x^6+4*exp(3*x)*x^5+exp(4*x)*x^4)/(exp(4*x)+4*x*exp(3*x)+6*exp(2*x)*x^2+4*exp(x)*x^3
+x^4))
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maxima [B] time = 2.88, size = 217, normalized size = 8.04 \begin {gather*} x e^{\left (x^{4} + 4 \, x^{3} + 2 \, x^{2} + 4 \, x e^{x} - 9 \, x + \frac {4 \, e^{\left (3 \, x\right )}}{x + e^{x}} + \frac {6 \, e^{\left (2 \, x\right )}}{x^{2} + 2 \, x e^{x} + e^{\left (2 \, x\right )}} - \frac {12 \, e^{\left (2 \, x\right )}}{x + e^{x}} + \frac {4 \, e^{x}}{x^{3} + 3 \, x^{2} e^{x} + 3 \, x e^{\left (2 \, x\right )} + e^{\left (3 \, x\right )}} - \frac {12 \, e^{x}}{x^{2} + 2 \, x e^{x} + e^{\left (2 \, x\right )}} + \frac {1}{x^{4} + 4 \, x^{3} e^{x} + 6 \, x^{2} e^{\left (2 \, x\right )} + 4 \, x e^{\left (3 \, x\right )} + e^{\left (4 \, x\right )}} - \frac {4}{x^{3} + 3 \, x^{2} e^{x} + 3 \, x e^{\left (2 \, x\right )} + e^{\left (3 \, x\right )}} + \frac {2}{x^{2} + 2 \, x e^{x} + e^{\left (2 \, x\right )}} + \frac {8}{x + e^{x}} - 4 \, e^{\left (2 \, x\right )} + 12 \, e^{x} - 5\right )} - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((4*x^5+12*x^4+12*x^3+3*x^2+x)*exp(x)^5+(20*x^6+64*x^5+60*x^4+3*x^3-3*x^2)*exp(x)^4+(40*x^7+132*x^6
+112*x^5-30*x^4-26*x^3+4*x^2)*exp(x)^3+(40*x^8+132*x^7+96*x^6-66*x^5-38*x^4+12*x^3-4*x^2)*exp(x)^2+(20*x^9+64*
x^8+36*x^7-45*x^6-15*x^5-8*x^3+8*x^2)*exp(x)+4*x^10+12*x^9+4*x^8-9*x^7+x^6-8*x^5-4*x^4+12*x^3-4*x^2)*exp(((x^4
+4*x^3+6*x^2+3*x+1)*exp(x)^4+(4*x^5+16*x^4+20*x^3-8*x-4)*exp(x)^3+(6*x^6+24*x^5+24*x^4-18*x^3-24*x^2+6)*exp(x)
^2+(4*x^7+16*x^6+12*x^5-24*x^4-20*x^3+12*x^2+8*x-4)*exp(x)+x^8+4*x^7+2*x^6-9*x^5-5*x^4+8*x^3+2*x^2-4*x+1)/(exp
(x)^4+4*x*exp(x)^3+6*exp(x)^2*x^2+4*exp(x)*x^3+x^4))-exp(x)^5-5*x*exp(x)^4-10*x^2*exp(x)^3-10*exp(x)^2*x^3-5*e
xp(x)*x^4-x^5)/(x*exp(x)^5+5*x^2*exp(x)^4+10*x^3*exp(x)^3+10*exp(x)^2*x^4+5*x^5*exp(x)+x^6),x, algorithm="maxi
ma")
[Out]
x*e^(x^4 + 4*x^3 + 2*x^2 + 4*x*e^x - 9*x + 4*e^(3*x)/(x + e^x) + 6*e^(2*x)/(x^2 + 2*x*e^x + e^(2*x)) - 12*e^(2
*x)/(x + e^x) + 4*e^x/(x^3 + 3*x^2*e^x + 3*x*e^(2*x) + e^(3*x)) - 12*e^x/(x^2 + 2*x*e^x + e^(2*x)) + 1/(x^4 +
4*x^3*e^x + 6*x^2*e^(2*x) + 4*x*e^(3*x) + e^(4*x)) - 4/(x^3 + 3*x^2*e^x + 3*x*e^(2*x) + e^(3*x)) + 2/(x^2 + 2*
x*e^x + e^(2*x)) + 8/(x + e^x) - 4*e^(2*x) + 12*e^x - 5) - log(x)
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mupad [B] time = 8.48, size = 1346, normalized size = 49.85 result too large to
display
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(-(exp(5*x) + 5*x*exp(4*x) + 5*x^4*exp(x) - exp((exp(2*x)*(24*x^4 - 18*x^3 - 24*x^2 + 24*x^5 + 6*x^6 + 6) -
4*x + exp(4*x)*(3*x + 6*x^2 + 4*x^3 + x^4 + 1) + exp(3*x)*(20*x^3 - 8*x + 16*x^4 + 4*x^5 - 4) + exp(x)*(8*x +
12*x^2 - 20*x^3 - 24*x^4 + 12*x^5 + 16*x^6 + 4*x^7 - 4) + 2*x^2 + 8*x^3 - 5*x^4 - 9*x^5 + 2*x^6 + 4*x^7 + x^8
+ 1)/(exp(4*x) + 4*x*exp(3*x) + 4*x^3*exp(x) + 6*x^2*exp(2*x) + x^4))*(exp(4*x)*(3*x^3 - 3*x^2 + 60*x^4 + 64*
x^5 + 20*x^6) + exp(x)*(8*x^2 - 8*x^3 - 15*x^5 - 45*x^6 + 36*x^7 + 64*x^8 + 20*x^9) + exp(3*x)*(4*x^2 - 26*x^3
- 30*x^4 + 112*x^5 + 132*x^6 + 40*x^7) + exp(5*x)*(x + 3*x^2 + 12*x^3 + 12*x^4 + 4*x^5) + exp(2*x)*(12*x^3 -
4*x^2 - 38*x^4 - 66*x^5 + 96*x^6 + 132*x^7 + 40*x^8) - 4*x^2 + 12*x^3 - 4*x^4 - 8*x^5 + x^6 - 9*x^7 + 4*x^8 +
12*x^9 + 4*x^10) + 10*x^2*exp(3*x) + 10*x^3*exp(2*x) + x^5)/(x*exp(5*x) + 5*x^5*exp(x) + 5*x^2*exp(4*x) + 10*x
^3*exp(3*x) + 10*x^4*exp(2*x) + x^6),x)
[Out]
x*exp((2*x^2)/(exp(4*x) + 4*x*exp(3*x) + 4*x^3*exp(x) + 6*x^2*exp(2*x) + x^4))*exp(x^8/(exp(4*x) + 4*x*exp(3*x
) + 4*x^3*exp(x) + 6*x^2*exp(2*x) + x^4))*exp((2*x^6)/(exp(4*x) + 4*x*exp(3*x) + 4*x^3*exp(x) + 6*x^2*exp(2*x)
+ x^4))*exp(-(5*x^4)/(exp(4*x) + 4*x*exp(3*x) + 4*x^3*exp(x) + 6*x^2*exp(2*x) + x^4))*exp((8*x^3)/(exp(4*x) +
4*x*exp(3*x) + 4*x^3*exp(x) + 6*x^2*exp(2*x) + x^4))*exp((4*x^7)/(exp(4*x) + 4*x*exp(3*x) + 4*x^3*exp(x) + 6*
x^2*exp(2*x) + x^4))*exp(-(9*x^5)/(exp(4*x) + 4*x*exp(3*x) + 4*x^3*exp(x) + 6*x^2*exp(2*x) + x^4))*exp(-(4*exp
(x))/(exp(4*x) + 4*x*exp(3*x) + 4*x^3*exp(x) + 6*x^2*exp(2*x) + x^4))*exp((x^4*exp(4*x))/(exp(4*x) + 4*x*exp(3
*x) + 4*x^3*exp(x) + 6*x^2*exp(2*x) + x^4))*exp((4*x^3*exp(4*x))/(exp(4*x) + 4*x*exp(3*x) + 4*x^3*exp(x) + 6*x
^2*exp(2*x) + x^4))*exp((6*x^2*exp(4*x))/(exp(4*x) + 4*x*exp(3*x) + 4*x^3*exp(x) + 6*x^2*exp(2*x) + x^4))*exp(
(4*x^5*exp(3*x))/(exp(4*x) + 4*x*exp(3*x) + 4*x^3*exp(x) + 6*x^2*exp(2*x) + x^4))*exp((6*x^6*exp(2*x))/(exp(4*
x) + 4*x*exp(3*x) + 4*x^3*exp(x) + 6*x^2*exp(2*x) + x^4))*exp(-(18*x^3*exp(2*x))/(exp(4*x) + 4*x*exp(3*x) + 4*
x^3*exp(x) + 6*x^2*exp(2*x) + x^4))*exp((16*x^4*exp(3*x))/(exp(4*x) + 4*x*exp(3*x) + 4*x^3*exp(x) + 6*x^2*exp(
2*x) + x^4))*exp((20*x^3*exp(3*x))/(exp(4*x) + 4*x*exp(3*x) + 4*x^3*exp(x) + 6*x^2*exp(2*x) + x^4))*exp(-(24*x
^2*exp(2*x))/(exp(4*x) + 4*x*exp(3*x) + 4*x^3*exp(x) + 6*x^2*exp(2*x) + x^4))*exp((24*x^4*exp(2*x))/(exp(4*x)
+ 4*x*exp(3*x) + 4*x^3*exp(x) + 6*x^2*exp(2*x) + x^4))*exp((24*x^5*exp(2*x))/(exp(4*x) + 4*x*exp(3*x) + 4*x^3*
exp(x) + 6*x^2*exp(2*x) + x^4))*exp(exp(4*x)/(exp(4*x) + 4*x*exp(3*x) + 4*x^3*exp(x) + 6*x^2*exp(2*x) + x^4))*
exp(-(4*exp(3*x))/(exp(4*x) + 4*x*exp(3*x) + 4*x^3*exp(x) + 6*x^2*exp(2*x) + x^4))*exp((6*exp(2*x))/(exp(4*x)
+ 4*x*exp(3*x) + 4*x^3*exp(x) + 6*x^2*exp(2*x) + x^4))*exp((8*x*exp(x))/(exp(4*x) + 4*x*exp(3*x) + 4*x^3*exp(x
) + 6*x^2*exp(2*x) + x^4))*exp(-(4*x)/(exp(4*x) + 4*x*exp(3*x) + 4*x^3*exp(x) + 6*x^2*exp(2*x) + x^4))*exp(1/(
exp(4*x) + 4*x*exp(3*x) + 4*x^3*exp(x) + 6*x^2*exp(2*x) + x^4))*exp((3*x*exp(4*x))/(exp(4*x) + 4*x*exp(3*x) +
4*x^3*exp(x) + 6*x^2*exp(2*x) + x^4))*exp(-(8*x*exp(3*x))/(exp(4*x) + 4*x*exp(3*x) + 4*x^3*exp(x) + 6*x^2*exp(
2*x) + x^4))*exp((4*x^7*exp(x))/(exp(4*x) + 4*x*exp(3*x) + 4*x^3*exp(x) + 6*x^2*exp(2*x) + x^4))*exp((12*x^2*e
xp(x))/(exp(4*x) + 4*x*exp(3*x) + 4*x^3*exp(x) + 6*x^2*exp(2*x) + x^4))*exp((12*x^5*exp(x))/(exp(4*x) + 4*x*ex
p(3*x) + 4*x^3*exp(x) + 6*x^2*exp(2*x) + x^4))*exp((16*x^6*exp(x))/(exp(4*x) + 4*x*exp(3*x) + 4*x^3*exp(x) + 6
*x^2*exp(2*x) + x^4))*exp(-(20*x^3*exp(x))/(exp(4*x) + 4*x*exp(3*x) + 4*x^3*exp(x) + 6*x^2*exp(2*x) + x^4))*ex
p(-(24*x^4*exp(x))/(exp(4*x) + 4*x*exp(3*x) + 4*x^3*exp(x) + 6*x^2*exp(2*x) + x^4)) - log(x)
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sympy [B] time = 75.79, size = 201, normalized size = 7.44 \begin {gather*} x e^{\frac {x^{8} + 4 x^{7} + 2 x^{6} - 9 x^{5} - 5 x^{4} + 8 x^{3} + 2 x^{2} - 4 x + \left (x^{4} + 4 x^{3} + 6 x^{2} + 3 x + 1\right ) e^{4 x} + \left (4 x^{5} + 16 x^{4} + 20 x^{3} - 8 x - 4\right ) e^{3 x} + \left (6 x^{6} + 24 x^{5} + 24 x^{4} - 18 x^{3} - 24 x^{2} + 6\right ) e^{2 x} + \left (4 x^{7} + 16 x^{6} + 12 x^{5} - 24 x^{4} - 20 x^{3} + 12 x^{2} + 8 x - 4\right ) e^{x} + 1}{x^{4} + 4 x^{3} e^{x} + 6 x^{2} e^{2 x} + 4 x e^{3 x} + e^{4 x}}} - \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((4*x**5+12*x**4+12*x**3+3*x**2+x)*exp(x)**5+(20*x**6+64*x**5+60*x**4+3*x**3-3*x**2)*exp(x)**4+(40*
x**7+132*x**6+112*x**5-30*x**4-26*x**3+4*x**2)*exp(x)**3+(40*x**8+132*x**7+96*x**6-66*x**5-38*x**4+12*x**3-4*x
**2)*exp(x)**2+(20*x**9+64*x**8+36*x**7-45*x**6-15*x**5-8*x**3+8*x**2)*exp(x)+4*x**10+12*x**9+4*x**8-9*x**7+x*
*6-8*x**5-4*x**4+12*x**3-4*x**2)*exp(((x**4+4*x**3+6*x**2+3*x+1)*exp(x)**4+(4*x**5+16*x**4+20*x**3-8*x-4)*exp(
x)**3+(6*x**6+24*x**5+24*x**4-18*x**3-24*x**2+6)*exp(x)**2+(4*x**7+16*x**6+12*x**5-24*x**4-20*x**3+12*x**2+8*x
-4)*exp(x)+x**8+4*x**7+2*x**6-9*x**5-5*x**4+8*x**3+2*x**2-4*x+1)/(exp(x)**4+4*x*exp(x)**3+6*exp(x)**2*x**2+4*e
xp(x)*x**3+x**4))-exp(x)**5-5*x*exp(x)**4-10*x**2*exp(x)**3-10*exp(x)**2*x**3-5*exp(x)*x**4-x**5)/(x*exp(x)**5
+5*x**2*exp(x)**4+10*x**3*exp(x)**3+10*exp(x)**2*x**4+5*x**5*exp(x)+x**6),x)
[Out]
x*exp((x**8 + 4*x**7 + 2*x**6 - 9*x**5 - 5*x**4 + 8*x**3 + 2*x**2 - 4*x + (x**4 + 4*x**3 + 6*x**2 + 3*x + 1)*e
xp(4*x) + (4*x**5 + 16*x**4 + 20*x**3 - 8*x - 4)*exp(3*x) + (6*x**6 + 24*x**5 + 24*x**4 - 18*x**3 - 24*x**2 +
6)*exp(2*x) + (4*x**7 + 16*x**6 + 12*x**5 - 24*x**4 - 20*x**3 + 12*x**2 + 8*x - 4)*exp(x) + 1)/(x**4 + 4*x**3*
exp(x) + 6*x**2*exp(2*x) + 4*x*exp(3*x) + exp(4*x))) - log(x)
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