3.52.17 \(\int \frac {e^{\frac {2 (4 x^2+e^x (4 x^2-4 x^3)+e^{2 x} (-e^3+x^2-2 x^3+x^4)+(4 x^2-4 x^3+e^x (-2 e^3+2 x^2-4 x^3+2 x^4)) \log (x)+(-e^3+x^2-2 x^3+x^4) \log ^2(x))}{e^{2 x}+2 e^x \log (x)+\log ^2(x)}} (-16 x+e^x (8 x-8 x^2)+e^{2 x} (16 x-32 x^2+8 x^3)+e^{3 x} (4 x-12 x^2+8 x^3)+(8 x+8 x^2+e^x (32 x-56 x^2+8 x^3)+e^{2 x} (12 x-36 x^2+24 x^3)) \log (x)+(16 x-24 x^2+e^x (12 x-36 x^2+24 x^3)) \log ^2(x)+(4 x-12 x^2+8 x^3) \log ^3(x))}{e^{3 x}+3 e^{2 x} \log (x)+3 e^x \log ^2(x)+\log ^3(x)} \, dx\)

Optimal. Leaf size=30 \[ e^{-2 e^3+2 \left (x-x^2+\frac {2 x}{e^x+\log (x)}\right )^2} \]

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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^((2*(4*x^2 + E^x*(4*x^2 - 4*x^3) + E^(2*x)*(-E^3 + x^2 - 2*x^3 + x^4) + (4*x^2 - 4*x^3 + E^x*(-2*E^3 +
2*x^2 - 4*x^3 + 2*x^4))*Log[x] + (-E^3 + x^2 - 2*x^3 + x^4)*Log[x]^2))/(E^(2*x) + 2*E^x*Log[x] + Log[x]^2))*(-
16*x + E^x*(8*x - 8*x^2) + E^(2*x)*(16*x - 32*x^2 + 8*x^3) + E^(3*x)*(4*x - 12*x^2 + 8*x^3) + (8*x + 8*x^2 + E
^x*(32*x - 56*x^2 + 8*x^3) + E^(2*x)*(12*x - 36*x^2 + 24*x^3))*Log[x] + (16*x - 24*x^2 + E^x*(12*x - 36*x^2 +
24*x^3))*Log[x]^2 + (4*x - 12*x^2 + 8*x^3)*Log[x]^3))/(E^(3*x) + 3*E^(2*x)*Log[x] + 3*E^x*Log[x]^2 + Log[x]^3)
,x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [B]  time = 1.93, size = 110, normalized size = 3.67 \begin {gather*} e^{-\frac {2 \left (e^{3+2 x}-4 x^2+4 e^x (-1+x) x^2-e^{2 x} (-1+x)^2 x^2+\left (e^3-(-1+x)^2 x^2\right ) \log ^2(x)\right )}{\left (e^x+\log (x)\right )^2}} x^{-\frac {4 \left (e^{3+x}+2 (-1+x) x^2-e^x (-1+x)^2 x^2\right )}{\left (e^x+\log (x)\right )^2}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((2*(4*x^2 + E^x*(4*x^2 - 4*x^3) + E^(2*x)*(-E^3 + x^2 - 2*x^3 + x^4) + (4*x^2 - 4*x^3 + E^x*(-2*
E^3 + 2*x^2 - 4*x^3 + 2*x^4))*Log[x] + (-E^3 + x^2 - 2*x^3 + x^4)*Log[x]^2))/(E^(2*x) + 2*E^x*Log[x] + Log[x]^
2))*(-16*x + E^x*(8*x - 8*x^2) + E^(2*x)*(16*x - 32*x^2 + 8*x^3) + E^(3*x)*(4*x - 12*x^2 + 8*x^3) + (8*x + 8*x
^2 + E^x*(32*x - 56*x^2 + 8*x^3) + E^(2*x)*(12*x - 36*x^2 + 24*x^3))*Log[x] + (16*x - 24*x^2 + E^x*(12*x - 36*
x^2 + 24*x^3))*Log[x]^2 + (4*x - 12*x^2 + 8*x^3)*Log[x]^3))/(E^(3*x) + 3*E^(2*x)*Log[x] + 3*E^x*Log[x]^2 + Log
[x]^3),x]

[Out]

1/(E^((2*(E^(3 + 2*x) - 4*x^2 + 4*E^x*(-1 + x)*x^2 - E^(2*x)*(-1 + x)^2*x^2 + (E^3 - (-1 + x)^2*x^2)*Log[x]^2)
)/(E^x + Log[x])^2)*x^((4*(E^(3 + x) + 2*(-1 + x)*x^2 - E^x*(-1 + x)^2*x^2))/(E^x + Log[x])^2))

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fricas [B]  time = 0.50, size = 116, normalized size = 3.87 \begin {gather*} e^{\left (\frac {2 \, {\left ({\left (x^{4} - 2 \, x^{3} + x^{2} - e^{3}\right )} \log \relax (x)^{2} + 4 \, x^{2} + {\left (x^{4} - 2 \, x^{3} + x^{2} - e^{3}\right )} e^{\left (2 \, x\right )} - 4 \, {\left (x^{3} - x^{2}\right )} e^{x} - 2 \, {\left (2 \, x^{3} - 2 \, x^{2} - {\left (x^{4} - 2 \, x^{3} + x^{2} - e^{3}\right )} e^{x}\right )} \log \relax (x)\right )}}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((8*x^3-12*x^2+4*x)*log(x)^3+((24*x^3-36*x^2+12*x)*exp(x)-24*x^2+16*x)*log(x)^2+((24*x^3-36*x^2+12*x
)*exp(x)^2+(8*x^3-56*x^2+32*x)*exp(x)+8*x^2+8*x)*log(x)+(8*x^3-12*x^2+4*x)*exp(x)^3+(8*x^3-32*x^2+16*x)*exp(x)
^2+(-8*x^2+8*x)*exp(x)-16*x)*exp(((-exp(3)+x^4-2*x^3+x^2)*log(x)^2+((-2*exp(3)+2*x^4-4*x^3+2*x^2)*exp(x)-4*x^3
+4*x^2)*log(x)+(-exp(3)+x^4-2*x^3+x^2)*exp(x)^2+(-4*x^3+4*x^2)*exp(x)+4*x^2)/(log(x)^2+2*exp(x)*log(x)+exp(x)^
2))^2/(log(x)^3+3*exp(x)*log(x)^2+3*exp(x)^2*log(x)+exp(x)^3),x, algorithm="fricas")

[Out]

e^(2*((x^4 - 2*x^3 + x^2 - e^3)*log(x)^2 + 4*x^2 + (x^4 - 2*x^3 + x^2 - e^3)*e^(2*x) - 4*(x^3 - x^2)*e^x - 2*(
2*x^3 - 2*x^2 - (x^4 - 2*x^3 + x^2 - e^3)*e^x)*log(x))/(2*e^x*log(x) + log(x)^2 + e^(2*x)))

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giac [B]  time = 7.80, size = 155, normalized size = 5.17 \begin {gather*} e^{\left (\frac {2 \, {\left (2 \, x^{4} e^{x} \log \relax (x) + x^{4} \log \relax (x)^{2} + x^{4} e^{\left (2 \, x\right )} - 4 \, x^{3} e^{x} \log \relax (x) - 2 \, x^{3} \log \relax (x)^{2} - 2 \, x^{3} e^{\left (2 \, x\right )} - 4 \, x^{3} e^{x} - 4 \, x^{3} \log \relax (x) + 2 \, x^{2} e^{x} \log \relax (x) + x^{2} \log \relax (x)^{2} + x^{2} e^{\left (2 \, x\right )} + 4 \, x^{2} e^{x} + 4 \, x^{2} \log \relax (x) - e^{3} \log \relax (x)^{2} + 4 \, x^{2} - 2 \, e^{\left (x + 3\right )} \log \relax (x) - e^{\left (2 \, x + 3\right )}\right )}}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((8*x^3-12*x^2+4*x)*log(x)^3+((24*x^3-36*x^2+12*x)*exp(x)-24*x^2+16*x)*log(x)^2+((24*x^3-36*x^2+12*x
)*exp(x)^2+(8*x^3-56*x^2+32*x)*exp(x)+8*x^2+8*x)*log(x)+(8*x^3-12*x^2+4*x)*exp(x)^3+(8*x^3-32*x^2+16*x)*exp(x)
^2+(-8*x^2+8*x)*exp(x)-16*x)*exp(((-exp(3)+x^4-2*x^3+x^2)*log(x)^2+((-2*exp(3)+2*x^4-4*x^3+2*x^2)*exp(x)-4*x^3
+4*x^2)*log(x)+(-exp(3)+x^4-2*x^3+x^2)*exp(x)^2+(-4*x^3+4*x^2)*exp(x)+4*x^2)/(log(x)^2+2*exp(x)*log(x)+exp(x)^
2))^2/(log(x)^3+3*exp(x)*log(x)^2+3*exp(x)^2*log(x)+exp(x)^3),x, algorithm="giac")

[Out]

e^(2*(2*x^4*e^x*log(x) + x^4*log(x)^2 + x^4*e^(2*x) - 4*x^3*e^x*log(x) - 2*x^3*log(x)^2 - 2*x^3*e^(2*x) - 4*x^
3*e^x - 4*x^3*log(x) + 2*x^2*e^x*log(x) + x^2*log(x)^2 + x^2*e^(2*x) + 4*x^2*e^x + 4*x^2*log(x) - e^3*log(x)^2
+ 4*x^2 - 2*e^(x + 3)*log(x) - e^(2*x + 3))/(2*e^x*log(x) + log(x)^2 + e^(2*x)))

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maple [B]  time = 0.13, size = 157, normalized size = 5.23

method	result	size
risch	\({\mathrm e}^{-\frac {2 \left (-x^{4} \ln \relax (x )^{2}-2 x^{4} {\mathrm e}^{x} \ln \relax (x )+2 x^{3} \ln \relax (x )^{2}+4 x^{3} {\mathrm e}^{x} \ln \relax (x )-{\mathrm e}^{2 x} x^{4}-x^{2} \ln \relax (x )^{2}-2 x^{2} {\mathrm e}^{x} \ln \relax (x )+4 x^{3} \ln \relax (x )+4 \,{\mathrm e}^{x} x^{3}+2 \,{\mathrm e}^{2 x} x^{3}+{\mathrm e}^{3} \ln \relax (x )^{2}+2 \ln \relax (x ) {\mathrm e}^{3+x}-4 x^{2} \ln \relax (x )-4 \,{\mathrm e}^{x} x^{2}-{\mathrm e}^{2 x} x^{2}+{\mathrm e}^{2 x +3}-4 x^{2}\right )}{\ln \relax (x )^{2}+2 \,{\mathrm e}^{x} \ln \relax (x )+{\mathrm e}^{2 x}}}\)	\(157\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((8*x^3-12*x^2+4*x)*ln(x)^3+((24*x^3-36*x^2+12*x)*exp(x)-24*x^2+16*x)*ln(x)^2+((24*x^3-36*x^2+12*x)*exp(x)
^2+(8*x^3-56*x^2+32*x)*exp(x)+8*x^2+8*x)*ln(x)+(8*x^3-12*x^2+4*x)*exp(x)^3+(8*x^3-32*x^2+16*x)*exp(x)^2+(-8*x^
2+8*x)*exp(x)-16*x)*exp(((-exp(3)+x^4-2*x^3+x^2)*ln(x)^2+((-2*exp(3)+2*x^4-4*x^3+2*x^2)*exp(x)-4*x^3+4*x^2)*ln
(x)+(-exp(3)+x^4-2*x^3+x^2)*exp(x)^2+(-4*x^3+4*x^2)*exp(x)+4*x^2)/(ln(x)^2+2*exp(x)*ln(x)+exp(x)^2))^2/(ln(x)^
3+3*exp(x)*ln(x)^2+3*exp(x)^2*ln(x)+exp(x)^3),x,method=_RETURNVERBOSE)

[Out]

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

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maxima [B]  time = 2.17, size = 429, normalized size = 14.30 \begin {gather*} e^{\left (\frac {4 \, x^{4} e^{x} \log \relax (x)}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} + \frac {2 \, x^{4} \log \relax (x)^{2}}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} + \frac {2 \, x^{4} e^{\left (2 \, x\right )}}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} - \frac {8 \, x^{3} e^{x} \log \relax (x)}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} - \frac {4 \, x^{3} \log \relax (x)^{2}}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} - \frac {4 \, x^{3} e^{\left (2 \, x\right )}}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} - \frac {8 \, x^{3} e^{x}}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} - \frac {8 \, x^{3} \log \relax (x)}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} + \frac {4 \, x^{2} e^{x} \log \relax (x)}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} + \frac {2 \, x^{2} \log \relax (x)^{2}}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} + \frac {2 \, x^{2} e^{\left (2 \, x\right )}}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} + \frac {8 \, x^{2} e^{x}}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} + \frac {8 \, x^{2} \log \relax (x)}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} - \frac {2 \, e^{3} \log \relax (x)^{2}}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} + \frac {8 \, x^{2}}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} - \frac {4 \, e^{\left (x + 3\right )} \log \relax (x)}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}} - \frac {2 \, e^{\left (2 \, x + 3\right )}}{2 \, e^{x} \log \relax (x) + \log \relax (x)^{2} + e^{\left (2 \, x\right )}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((8*x^3-12*x^2+4*x)*log(x)^3+((24*x^3-36*x^2+12*x)*exp(x)-24*x^2+16*x)*log(x)^2+((24*x^3-36*x^2+12*x
)*exp(x)^2+(8*x^3-56*x^2+32*x)*exp(x)+8*x^2+8*x)*log(x)+(8*x^3-12*x^2+4*x)*exp(x)^3+(8*x^3-32*x^2+16*x)*exp(x)
^2+(-8*x^2+8*x)*exp(x)-16*x)*exp(((-exp(3)+x^4-2*x^3+x^2)*log(x)^2+((-2*exp(3)+2*x^4-4*x^3+2*x^2)*exp(x)-4*x^3
+4*x^2)*log(x)+(-exp(3)+x^4-2*x^3+x^2)*exp(x)^2+(-4*x^3+4*x^2)*exp(x)+4*x^2)/(log(x)^2+2*exp(x)*log(x)+exp(x)^
2))^2/(log(x)^3+3*exp(x)*log(x)^2+3*exp(x)^2*log(x)+exp(x)^3),x, algorithm="maxima")

[Out]

e^(4*x^4*e^x*log(x)/(2*e^x*log(x) + log(x)^2 + e^(2*x)) + 2*x^4*log(x)^2/(2*e^x*log(x) + log(x)^2 + e^(2*x)) +
2*x^4*e^(2*x)/(2*e^x*log(x) + log(x)^2 + e^(2*x)) - 8*x^3*e^x*log(x)/(2*e^x*log(x) + log(x)^2 + e^(2*x)) - 4*
x^3*log(x)^2/(2*e^x*log(x) + log(x)^2 + e^(2*x)) - 4*x^3*e^(2*x)/(2*e^x*log(x) + log(x)^2 + e^(2*x)) - 8*x^3*e
^x/(2*e^x*log(x) + log(x)^2 + e^(2*x)) - 8*x^3*log(x)/(2*e^x*log(x) + log(x)^2 + e^(2*x)) + 4*x^2*e^x*log(x)/(
2*e^x*log(x) + log(x)^2 + e^(2*x)) + 2*x^2*log(x)^2/(2*e^x*log(x) + log(x)^2 + e^(2*x)) + 2*x^2*e^(2*x)/(2*e^x
*log(x) + log(x)^2 + e^(2*x)) + 8*x^2*e^x/(2*e^x*log(x) + log(x)^2 + e^(2*x)) + 8*x^2*log(x)/(2*e^x*log(x) + l
og(x)^2 + e^(2*x)) - 2*e^3*log(x)^2/(2*e^x*log(x) + log(x)^2 + e^(2*x)) + 8*x^2/(2*e^x*log(x) + log(x)^2 + e^(
2*x)) - 4*e^(x + 3)*log(x)/(2*e^x*log(x) + log(x)^2 + e^(2*x)) - 2*e^(2*x + 3)/(2*e^x*log(x) + log(x)^2 + e^(2
*x)))

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mupad [B]  time = 3.87, size = 345, normalized size = 11.50 \begin {gather*} x^{\frac {4\,\left (x^2\,{\mathrm {e}}^x-2\,x^3\,{\mathrm {e}}^x+x^4\,{\mathrm {e}}^x-{\mathrm {e}}^3\,{\mathrm {e}}^x+2\,x^2-2\,x^3\right )}{{\ln \relax (x)}^2+2\,{\mathrm {e}}^x\,\ln \relax (x)+{\mathrm {e}}^{2\,x}}}\,{\mathrm {e}}^{\frac {2\,x^2\,{\mathrm {e}}^{2\,x}}{{\ln \relax (x)}^2+2\,{\mathrm {e}}^x\,\ln \relax (x)+{\mathrm {e}}^{2\,x}}}\,{\mathrm {e}}^{\frac {2\,x^4\,{\mathrm {e}}^{2\,x}}{{\ln \relax (x)}^2+2\,{\mathrm {e}}^x\,\ln \relax (x)+{\mathrm {e}}^{2\,x}}}\,{\mathrm {e}}^{-\frac {4\,x^3\,{\mathrm {e}}^{2\,x}}{{\ln \relax (x)}^2+2\,{\mathrm {e}}^x\,\ln \relax (x)+{\mathrm {e}}^{2\,x}}}\,{\mathrm {e}}^{\frac {2\,x^2\,{\ln \relax (x)}^2}{{\ln \relax (x)}^2+2\,{\mathrm {e}}^x\,\ln \relax (x)+{\mathrm {e}}^{2\,x}}}\,{\mathrm {e}}^{\frac {2\,x^4\,{\ln \relax (x)}^2}{{\ln \relax (x)}^2+2\,{\mathrm {e}}^x\,\ln \relax (x)+{\mathrm {e}}^{2\,x}}}\,{\mathrm {e}}^{-\frac {4\,x^3\,{\ln \relax (x)}^2}{{\ln \relax (x)}^2+2\,{\mathrm {e}}^x\,\ln \relax (x)+{\mathrm {e}}^{2\,x}}}\,{\mathrm {e}}^{-\frac {2\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^3}{{\ln \relax (x)}^2+2\,{\mathrm {e}}^x\,\ln \relax (x)+{\mathrm {e}}^{2\,x}}}\,{\mathrm {e}}^{-\frac {2\,{\mathrm {e}}^3\,{\ln \relax (x)}^2}{{\ln \relax (x)}^2+2\,{\mathrm {e}}^x\,\ln \relax (x)+{\mathrm {e}}^{2\,x}}}\,{\mathrm {e}}^{\frac {8\,x^2\,{\mathrm {e}}^x}{{\ln \relax (x)}^2+2\,{\mathrm {e}}^x\,\ln \relax (x)+{\mathrm {e}}^{2\,x}}}\,{\mathrm {e}}^{-\frac {8\,x^3\,{\mathrm {e}}^x}{{\ln \relax (x)}^2+2\,{\mathrm {e}}^x\,\ln \relax (x)+{\mathrm {e}}^{2\,x}}}\,{\mathrm {e}}^{\frac {8\,x^2}{{\ln \relax (x)}^2+2\,{\mathrm {e}}^x\,\ln \relax (x)+{\mathrm {e}}^{2\,x}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(-(2*(exp(2*x)*(exp(3) - x^2 + 2*x^3 - x^4) - exp(x)*(4*x^2 - 4*x^3) + log(x)^2*(exp(3) - x^2 + 2*x^3
- x^4) + log(x)*(exp(x)*(2*exp(3) - 2*x^2 + 4*x^3 - 2*x^4) - 4*x^2 + 4*x^3) - 4*x^2))/(exp(2*x) + 2*exp(x)*log
(x) + log(x)^2))*(exp(3*x)*(4*x - 12*x^2 + 8*x^3) - 16*x + exp(2*x)*(16*x - 32*x^2 + 8*x^3) + log(x)^3*(4*x -
12*x^2 + 8*x^3) + exp(x)*(8*x - 8*x^2) + log(x)*(8*x + exp(2*x)*(12*x - 36*x^2 + 24*x^3) + 8*x^2 + exp(x)*(32*
x - 56*x^2 + 8*x^3)) + log(x)^2*(16*x - 24*x^2 + exp(x)*(12*x - 36*x^2 + 24*x^3))))/(exp(3*x) + log(x)^3 + 3*e
xp(2*x)*log(x) + 3*exp(x)*log(x)^2),x)

[Out]

x^((4*(x^2*exp(x) - 2*x^3*exp(x) + x^4*exp(x) - exp(3)*exp(x) + 2*x^2 - 2*x^3))/(exp(2*x) + 2*exp(x)*log(x) +
log(x)^2))*exp((2*x^2*exp(2*x))/(exp(2*x) + 2*exp(x)*log(x) + log(x)^2))*exp((2*x^4*exp(2*x))/(exp(2*x) + 2*ex
p(x)*log(x) + log(x)^2))*exp(-(4*x^3*exp(2*x))/(exp(2*x) + 2*exp(x)*log(x) + log(x)^2))*exp((2*x^2*log(x)^2)/(
exp(2*x) + 2*exp(x)*log(x) + log(x)^2))*exp((2*x^4*log(x)^2)/(exp(2*x) + 2*exp(x)*log(x) + log(x)^2))*exp(-(4*
x^3*log(x)^2)/(exp(2*x) + 2*exp(x)*log(x) + log(x)^2))*exp(-(2*exp(2*x)*exp(3))/(exp(2*x) + 2*exp(x)*log(x) +
log(x)^2))*exp(-(2*exp(3)*log(x)^2)/(exp(2*x) + 2*exp(x)*log(x) + log(x)^2))*exp((8*x^2*exp(x))/(exp(2*x) + 2*
exp(x)*log(x) + log(x)^2))*exp(-(8*x^3*exp(x))/(exp(2*x) + 2*exp(x)*log(x) + log(x)^2))*exp((8*x^2)/(exp(2*x)
+ 2*exp(x)*log(x) + log(x)^2))

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sympy [B]  time = 2.40, size = 122, normalized size = 4.07 \begin {gather*} e^{\frac {2 \left (4 x^{2} + \left (- 4 x^{3} + 4 x^{2}\right ) e^{x} + \left (- 4 x^{3} + 4 x^{2} + \left (2 x^{4} - 4 x^{3} + 2 x^{2} - 2 e^{3}\right ) e^{x}\right ) \log {\relax (x )} + \left (x^{4} - 2 x^{3} + x^{2} - e^{3}\right ) e^{2 x} + \left (x^{4} - 2 x^{3} + x^{2} - e^{3}\right ) \log {\relax (x )}^{2}\right )}{e^{2 x} + 2 e^{x} \log {\relax (x )} + \log {\relax (x )}^{2}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((8*x**3-12*x**2+4*x)*ln(x)**3+((24*x**3-36*x**2+12*x)*exp(x)-24*x**2+16*x)*ln(x)**2+((24*x**3-36*x*
*2+12*x)*exp(x)**2+(8*x**3-56*x**2+32*x)*exp(x)+8*x**2+8*x)*ln(x)+(8*x**3-12*x**2+4*x)*exp(x)**3+(8*x**3-32*x*
*2+16*x)*exp(x)**2+(-8*x**2+8*x)*exp(x)-16*x)*exp(((-exp(3)+x**4-2*x**3+x**2)*ln(x)**2+((-2*exp(3)+2*x**4-4*x*
*3+2*x**2)*exp(x)-4*x**3+4*x**2)*ln(x)+(-exp(3)+x**4-2*x**3+x**2)*exp(x)**2+(-4*x**3+4*x**2)*exp(x)+4*x**2)/(l
n(x)**2+2*exp(x)*ln(x)+exp(x)**2))**2/(ln(x)**3+3*exp(x)*ln(x)**2+3*exp(x)**2*ln(x)+exp(x)**3),x)

[Out]

exp(2*(4*x**2 + (-4*x**3 + 4*x**2)*exp(x) + (-4*x**3 + 4*x**2 + (2*x**4 - 4*x**3 + 2*x**2 - 2*exp(3))*exp(x))*
log(x) + (x**4 - 2*x**3 + x**2 - exp(3))*exp(2*x) + (x**4 - 2*x**3 + x**2 - exp(3))*log(x)**2)/(exp(2*x) + 2*e
xp(x)*log(x) + log(x)**2))

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