3.61.48 \(\int \frac {1}{5} e^{e^{e^x x}+x+e^x x} (-1-x) \, dx\) [6048]

Optimal. Leaf size=27 \[ \frac {1}{12}+\frac {1}{5} \left (-6-e^{e^{e^x x}}-\log ^2(4)\right ) \]

[Out]

-67/60-4/5*ln(2)^2-1/5*exp(exp(exp(x)*x))

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Rubi [F]
time = 0.15, 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}{5} e^{e^{e^x x}+x+e^x x} (-1-x) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(E^(E^x*x) + x + E^x*x)*(-1 - x))/5,x]

[Out]

-1/5*Defer[Int][E^(E^(E^x*x) + x + E^x*x), x] - Defer[Int][E^(E^(E^x*x) + x + E^x*x)*x, x]/5

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int e^{e^{e^x x}+x+e^x x} (-1-x) \, dx\\ &=\frac {1}{5} \int \left (-e^{e^{e^x x}+x+e^x x}-e^{e^{e^x x}+x+e^x x} x\right ) \, dx\\ &=-\left (\frac {1}{5} \int e^{e^{e^x x}+x+e^x x} \, dx\right )-\frac {1}{5} \int e^{e^{e^x x}+x+e^x x} x \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.08, size = 13, normalized size = 0.48 \begin {gather*} -\frac {1}{5} e^{e^{e^x x}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(E^(E^x*x) + x + E^x*x)*(-1 - x))/5,x]

[Out]

-1/5*E^E^(E^x*x)

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Maple [A]
time = 0.10, size = 9, normalized size = 0.33

method	result	size
norman	\(-\frac {{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x} x}}}{5}\)	\(9\)
risch	\(-\frac {{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x} x}}}{5}\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/5*(-x-1)*exp(x)*exp(exp(x)*x)*exp(exp(exp(x)*x)),x,method=_RETURNVERBOSE)

[Out]

-1/5*exp(exp(exp(x)*x))

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Maxima [A]
time = 0.34, size = 8, normalized size = 0.30 \begin {gather*} -\frac {1}{5} \, e^{\left (e^{\left (x e^{x}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*(-1-x)*exp(x)*exp(exp(x)*x)*exp(exp(exp(x)*x)),x, algorithm="maxima")

[Out]

-1/5*e^(e^(x*e^x))

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Fricas [A]
time = 0.41, size = 8, normalized size = 0.30 \begin {gather*} -\frac {1}{5} \, e^{\left (e^{\left (x e^{x}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*(-1-x)*exp(x)*exp(exp(x)*x)*exp(exp(exp(x)*x)),x, algorithm="fricas")

[Out]

-1/5*e^(e^(x*e^x))

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Sympy [A]
time = 0.17, size = 10, normalized size = 0.37 \begin {gather*} - \frac {e^{e^{x e^{x}}}}{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*(-1-x)*exp(x)*exp(exp(x)*x)*exp(exp(exp(x)*x)),x)

[Out]

-exp(exp(x*exp(x)))/5

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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*(-1-x)*exp(x)*exp(exp(x)*x)*exp(exp(exp(x)*x)),x, algorithm="giac")

[Out]

integrate(-1/5*(x + 1)*e^(x*e^x + x + e^(x*e^x)), x)

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Mupad [B]
time = 4.95, size = 8, normalized size = 0.30 \begin {gather*} -\frac {{\mathrm {e}}^{{\mathrm {e}}^{x\,{\mathrm {e}}^x}}}{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(x*exp(x))*exp(exp(x*exp(x)))*exp(x)*(x + 1))/5,x)

[Out]

-exp(exp(x*exp(x)))/5

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