3.4.5 \(\int \frac {e^{e^{\frac {-5 x^2-x^3}{32-8 x^2+8 x^3}} (-1+x)+x-x^2} (64-128 x-32 x^2+96 x^3-60 x^4-16 x^5+20 x^6-8 x^7+e^{\frac {-5 x^2-x^3}{32-8 x^2+8 x^3}} (64+20 x-46 x^2+26 x^3+x^4-5 x^5+4 x^6))}{64-32 x^2+32 x^3+4 x^4-8 x^5+4 x^6} \, dx\)

Optimal. Leaf size=33 \[ e^{(1-x) \left (-e^{\frac {5+x}{8 \left (1-\frac {4}{x^2}-x\right )}}+x\right )} \]

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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^(E^((-5*x^2 - x^3)/(32 - 8*x^2 + 8*x^3))*(-1 + x) + x - x^2)*(64 - 128*x - 32*x^2 + 96*x^3 - 60*x^4 - 1
6*x^5 + 20*x^6 - 8*x^7 + E^((-5*x^2 - x^3)/(32 - 8*x^2 + 8*x^3))*(64 + 20*x - 46*x^2 + 26*x^3 + x^4 - 5*x^5 +
4*x^6)))/(64 - 32*x^2 + 32*x^3 + 4*x^4 - 8*x^5 + 4*x^6),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.24, size = 37, normalized size = 1.12 \begin {gather*} e^{e^{-\frac {x^2 (5+x)}{8 \left (4-x^2+x^3\right )}} (-1+x)+x-x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(E^((-5*x^2 - x^3)/(32 - 8*x^2 + 8*x^3))*(-1 + x) + x - x^2)*(64 - 128*x - 32*x^2 + 96*x^3 - 60*x
^4 - 16*x^5 + 20*x^6 - 8*x^7 + E^((-5*x^2 - x^3)/(32 - 8*x^2 + 8*x^3))*(64 + 20*x - 46*x^2 + 26*x^3 + x^4 - 5*
x^5 + 4*x^6)))/(64 - 32*x^2 + 32*x^3 + 4*x^4 - 8*x^5 + 4*x^6),x]

[Out]

E^((-1 + x)/E^((x^2*(5 + x))/(8*(4 - x^2 + x^3))) + x - x^2)

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fricas [A]  time = 0.76, size = 36, normalized size = 1.09 \begin {gather*} e^{\left (-x^{2} + {\left (x - 1\right )} e^{\left (-\frac {x^{3} + 5 \, x^{2}}{8 \, {\left (x^{3} - x^{2} + 4\right )}}\right )} + x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^6-5*x^5+x^4+26*x^3-46*x^2+20*x+64)*exp((-x^3-5*x^2)/(8*x^3-8*x^2+32))-8*x^7+20*x^6-16*x^5-60*x
^4+96*x^3-32*x^2-128*x+64)*exp((x-1)*exp((-x^3-5*x^2)/(8*x^3-8*x^2+32))-x^2+x)/(4*x^6-8*x^5+4*x^4+32*x^3-32*x^
2+64),x, algorithm="fricas")

[Out]

e^(-x^2 + (x - 1)*e^(-1/8*(x^3 + 5*x^2)/(x^3 - x^2 + 4)) + x)

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giac [B]  time = 2.67, size = 84, normalized size = 2.55 \begin {gather*} e^{\left (-x^{2} + x e^{\left (-\frac {x^{3}}{8 \, {\left (x^{3} - x^{2} + 4\right )}} - \frac {5 \, x^{2}}{8 \, {\left (x^{3} - x^{2} + 4\right )}}\right )} + x - e^{\left (-\frac {x^{3}}{8 \, {\left (x^{3} - x^{2} + 4\right )}} - \frac {5 \, x^{2}}{8 \, {\left (x^{3} - x^{2} + 4\right )}}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^6-5*x^5+x^4+26*x^3-46*x^2+20*x+64)*exp((-x^3-5*x^2)/(8*x^3-8*x^2+32))-8*x^7+20*x^6-16*x^5-60*x
^4+96*x^3-32*x^2-128*x+64)*exp((x-1)*exp((-x^3-5*x^2)/(8*x^3-8*x^2+32))-x^2+x)/(4*x^6-8*x^5+4*x^4+32*x^3-32*x^
2+64),x, algorithm="giac")

[Out]

e^(-x^2 + x*e^(-1/8*x^3/(x^3 - x^2 + 4) - 5/8*x^2/(x^3 - x^2 + 4)) + x - e^(-1/8*x^3/(x^3 - x^2 + 4) - 5/8*x^2
/(x^3 - x^2 + 4)))

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maple [A]  time = 0.19, size = 32, normalized size = 0.97

method	result	size
risch	\({\mathrm e}^{-\left (x -1\right ) \left (x -{\mathrm e}^{-\frac {x^{2} \left (5+x \right )}{8 \left (x^{3}-x^{2}+4\right )}}\right )}\)	\(32\)
norman	\(\frac {x^{3} {\mathrm e}^{\left (x -1\right ) {\mathrm e}^{\frac {-x^{3}-5 x^{2}}{8 x^{3}-8 x^{2}+32}}-x^{2}+x}-x^{2} {\mathrm e}^{\left (x -1\right ) {\mathrm e}^{\frac {-x^{3}-5 x^{2}}{8 x^{3}-8 x^{2}+32}}-x^{2}+x}+4 \,{\mathrm e}^{\left (x -1\right ) {\mathrm e}^{\frac {-x^{3}-5 x^{2}}{8 x^{3}-8 x^{2}+32}}-x^{2}+x}}{x^{3}-x^{2}+4}\)	\(143\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((4*x^6-5*x^5+x^4+26*x^3-46*x^2+20*x+64)*exp((-x^3-5*x^2)/(8*x^3-8*x^2+32))-8*x^7+20*x^6-16*x^5-60*x^4+96*
x^3-32*x^2-128*x+64)*exp((x-1)*exp((-x^3-5*x^2)/(8*x^3-8*x^2+32))-x^2+x)/(4*x^6-8*x^5+4*x^4+32*x^3-32*x^2+64),
x,method=_RETURNVERBOSE)

[Out]

exp(-(x-1)*(x-exp(-1/8*x^2*(5+x)/(x^3-x^2+4))))

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -\frac {1}{4} \, \int \frac {{\left (8 \, x^{7} - 20 \, x^{6} + 16 \, x^{5} + 60 \, x^{4} - 96 \, x^{3} + 32 \, x^{2} - {\left (4 \, x^{6} - 5 \, x^{5} + x^{4} + 26 \, x^{3} - 46 \, x^{2} + 20 \, x + 64\right )} e^{\left (-\frac {x^{3} + 5 \, x^{2}}{8 \, {\left (x^{3} - x^{2} + 4\right )}}\right )} + 128 \, x - 64\right )} e^{\left (-x^{2} + {\left (x - 1\right )} e^{\left (-\frac {x^{3} + 5 \, x^{2}}{8 \, {\left (x^{3} - x^{2} + 4\right )}}\right )} + x\right )}}{x^{6} - 2 \, x^{5} + x^{4} + 8 \, x^{3} - 8 \, x^{2} + 16}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x^6-5*x^5+x^4+26*x^3-46*x^2+20*x+64)*exp((-x^3-5*x^2)/(8*x^3-8*x^2+32))-8*x^7+20*x^6-16*x^5-60*x
^4+96*x^3-32*x^2-128*x+64)*exp((x-1)*exp((-x^3-5*x^2)/(8*x^3-8*x^2+32))-x^2+x)/(4*x^6-8*x^5+4*x^4+32*x^3-32*x^
2+64),x, algorithm="maxima")

[Out]

-1/4*integrate((8*x^7 - 20*x^6 + 16*x^5 + 60*x^4 - 96*x^3 + 32*x^2 - (4*x^6 - 5*x^5 + x^4 + 26*x^3 - 46*x^2 +
20*x + 64)*e^(-1/8*(x^3 + 5*x^2)/(x^3 - x^2 + 4)) + 128*x - 64)*e^(-x^2 + (x - 1)*e^(-1/8*(x^3 + 5*x^2)/(x^3 -
x^2 + 4)) + x)/(x^6 - 2*x^5 + x^4 + 8*x^3 - 8*x^2 + 16), x)

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mupad [B]  time = 0.69, size = 95, normalized size = 2.88 \begin {gather*} {\mathrm {e}}^{-{\mathrm {e}}^{-\frac {x^3}{8\,x^3-8\,x^2+32}}\,{\mathrm {e}}^{-\frac {5\,x^2}{8\,x^3-8\,x^2+32}}}\,{\mathrm {e}}^{-x^2}\,{\mathrm {e}}^{x\,{\mathrm {e}}^{-\frac {x^3}{8\,x^3-8\,x^2+32}}\,{\mathrm {e}}^{-\frac {5\,x^2}{8\,x^3-8\,x^2+32}}}\,{\mathrm {e}}^x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(x + exp(-(5*x^2 + x^3)/(8*x^3 - 8*x^2 + 32))*(x - 1) - x^2)*(128*x - exp(-(5*x^2 + x^3)/(8*x^3 - 8*x
^2 + 32))*(20*x - 46*x^2 + 26*x^3 + x^4 - 5*x^5 + 4*x^6 + 64) + 32*x^2 - 96*x^3 + 60*x^4 + 16*x^5 - 20*x^6 + 8
*x^7 - 64))/(32*x^3 - 32*x^2 + 4*x^4 - 8*x^5 + 4*x^6 + 64),x)

[Out]

exp(-exp(-x^3/(8*x^3 - 8*x^2 + 32))*exp(-(5*x^2)/(8*x^3 - 8*x^2 + 32)))*exp(-x^2)*exp(x*exp(-x^3/(8*x^3 - 8*x^
2 + 32))*exp(-(5*x^2)/(8*x^3 - 8*x^2 + 32)))*exp(x)

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sympy [A]  time = 2.47, size = 32, normalized size = 0.97 \begin {gather*} e^{- x^{2} + x + \left (x - 1\right ) e^{\frac {- x^{3} - 5 x^{2}}{8 x^{3} - 8 x^{2} + 32}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x**6-5*x**5+x**4+26*x**3-46*x**2+20*x+64)*exp((-x**3-5*x**2)/(8*x**3-8*x**2+32))-8*x**7+20*x**6-
16*x**5-60*x**4+96*x**3-32*x**2-128*x+64)*exp((x-1)*exp((-x**3-5*x**2)/(8*x**3-8*x**2+32))-x**2+x)/(4*x**6-8*x
**5+4*x**4+32*x**3-32*x**2+64),x)

[Out]

exp(-x**2 + x + (x - 1)*exp((-x**3 - 5*x**2)/(8*x**3 - 8*x**2 + 32)))

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