3.60.79 \(\int \frac {1}{2} e^{e^{\frac {1}{2} (14-2 e^4+2 e^{x^2}-x)}+\frac {1}{2} (14-2 e^4+2 e^{x^2}-x)} (-1+4 e^{x^2} x) \, dx\)

Optimal. Leaf size=21 \[ e^{e^{7-e^4+e^{x^2}-\frac {x}{2}}} \]

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Rubi [F]  time = 0.54, 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}{2} \exp \left (e^{\frac {1}{2} \left (14-2 e^4+2 e^{x^2}-x\right )}+\frac {1}{2} \left (14-2 e^4+2 e^{x^2}-x\right )\right ) \left (-1+4 e^{x^2} x\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(E^((14 - 2*E^4 + 2*E^x^2 - x)/2) + (14 - 2*E^4 + 2*E^x^2 - x)/2)*(-1 + 4*E^x^2*x))/2,x]

[Out]

-1/2*Defer[Int][E^(E^((14 - 2*E^4 + 2*E^x^2 - x)/2) + (14 - 2*E^4 + 2*E^x^2 - x)/2), x] + 2*Defer[Int][E^(E^((
14 - 2*E^4 + 2*E^x^2 - x)/2) + (14 - 2*E^4 + 2*E^x^2 - x)/2 + x^2)*x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \exp \left (e^{\frac {1}{2} \left (14-2 e^4+2 e^{x^2}-x\right )}+\frac {1}{2} \left (14-2 e^4+2 e^{x^2}-x\right )\right ) \left (-1+4 e^{x^2} x\right ) \, dx\\ &=\frac {1}{2} \int \left (-\exp \left (e^{\frac {1}{2} \left (14-2 e^4+2 e^{x^2}-x\right )}+\frac {1}{2} \left (14-2 e^4+2 e^{x^2}-x\right )\right )+4 \exp \left (e^{\frac {1}{2} \left (14-2 e^4+2 e^{x^2}-x\right )}+\frac {1}{2} \left (14-2 e^4+2 e^{x^2}-x\right )+x^2\right ) x\right ) \, dx\\ &=-\left (\frac {1}{2} \int \exp \left (e^{\frac {1}{2} \left (14-2 e^4+2 e^{x^2}-x\right )}+\frac {1}{2} \left (14-2 e^4+2 e^{x^2}-x\right )\right ) \, dx\right )+2 \int \exp \left (e^{\frac {1}{2} \left (14-2 e^4+2 e^{x^2}-x\right )}+\frac {1}{2} \left (14-2 e^4+2 e^{x^2}-x\right )+x^2\right ) x \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.32, size = 21, normalized size = 1.00 \begin {gather*} e^{e^{7-e^4+e^{x^2}-\frac {x}{2}}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(E^((14 - 2*E^4 + 2*E^x^2 - x)/2) + (14 - 2*E^4 + 2*E^x^2 - x)/2)*(-1 + 4*E^x^2*x))/2,x]

[Out]

E^E^(7 - E^4 + E^x^2 - x/2)

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fricas [A]  time = 0.60, size = 15, normalized size = 0.71 \begin {gather*} e^{\left (e^{\left (-\frac {1}{2} \, x - e^{4} + e^{\left (x^{2}\right )} + 7\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*(4*exp(x^2)*x-1)*exp(exp(x^2)-exp(4)-1/2*x+7)*exp(exp(exp(x^2)-exp(4)-1/2*x+7)),x, algorithm="fr
icas")

[Out]

e^(e^(-1/2*x - e^4 + e^(x^2) + 7))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{2} \, {\left (4 \, x e^{\left (x^{2}\right )} - 1\right )} e^{\left (-\frac {1}{2} \, x - e^{4} + e^{\left (x^{2}\right )} + e^{\left (-\frac {1}{2} \, x - e^{4} + e^{\left (x^{2}\right )} + 7\right )} + 7\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*(4*exp(x^2)*x-1)*exp(exp(x^2)-exp(4)-1/2*x+7)*exp(exp(exp(x^2)-exp(4)-1/2*x+7)),x, algorithm="gi
ac")

[Out]

integrate(1/2*(4*x*e^(x^2) - 1)*e^(-1/2*x - e^4 + e^(x^2) + e^(-1/2*x - e^4 + e^(x^2) + 7) + 7), x)

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maple [A]  time = 0.13, size = 16, normalized size = 0.76

method	result	size
norman	\({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}}-{\mathrm e}^{4}-\frac {x}{2}+7}}\)	\(16\)
risch	\({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}}-{\mathrm e}^{4}-\frac {x}{2}+7}}\)	\(16\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/2*(4*exp(x^2)*x-1)*exp(exp(x^2)-exp(4)-1/2*x+7)*exp(exp(exp(x^2)-exp(4)-1/2*x+7)),x,method=_RETURNVERBOS
E)

[Out]

exp(exp(exp(x^2)-exp(4)-1/2*x+7))

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maxima [A]  time = 0.81, size = 15, normalized size = 0.71 \begin {gather*} e^{\left (e^{\left (-\frac {1}{2} \, x - e^{4} + e^{\left (x^{2}\right )} + 7\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*(4*exp(x^2)*x-1)*exp(exp(x^2)-exp(4)-1/2*x+7)*exp(exp(exp(x^2)-exp(4)-1/2*x+7)),x, algorithm="ma
xima")

[Out]

e^(e^(-1/2*x - e^4 + e^(x^2) + 7))

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mupad [B]  time = 4.24, size = 18, normalized size = 0.86 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{-{\mathrm {e}}^4}\,{\mathrm {e}}^{-\frac {x}{2}}\,{\mathrm {e}}^7\,{\mathrm {e}}^{{\mathrm {e}}^{x^2}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(exp(exp(x^2) - x/2 - exp(4) + 7))*exp(exp(x^2) - x/2 - exp(4) + 7)*(4*x*exp(x^2) - 1))/2,x)

[Out]

exp(exp(-exp(4))*exp(-x/2)*exp(7)*exp(exp(x^2)))

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sympy [A]  time = 0.54, size = 15, normalized size = 0.71 \begin {gather*} e^{e^{- \frac {x}{2} + e^{x^{2}} - e^{4} + 7}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*(4*exp(x**2)*x-1)*exp(exp(x**2)-exp(4)-1/2*x+7)*exp(exp(exp(x**2)-exp(4)-1/2*x+7)),x)

[Out]

exp(exp(-x/2 + exp(x**2) - exp(4) + 7))

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