3.47.64 \(\int e^{x+e^x x} (-1-x) \, dx\)

Optimal. Leaf size=11 \[ 2-e^{e^x x} \]

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Rubi [F]  time = 0.10, 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 e^{x+e^x x} (-1-x) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[E^(x + E^x*x)*(-1 - x),x]

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 0.04, size = 9, normalized size = 0.82 \begin {gather*} -e^{e^x x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(x + E^x*x)*(-1 - x),x]

[Out]

-E^(E^x*x)

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fricas [A]  time = 0.69, size = 7, normalized size = 0.64 \begin {gather*} -e^{\left (x e^{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-e^(x*e^x)

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giac [A]  time = 0.14, size = 7, normalized size = 0.64 \begin {gather*} -e^{\left (x e^{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-e^(x*e^x)

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maple [A]  time = 0.03, size = 8, normalized size = 0.73

method	result	size
norman	\(-{\mathrm e}^{{\mathrm e}^{x} x}\)	\(8\)
risch	\(-{\mathrm e}^{{\mathrm e}^{x} x}\)	\(8\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-exp(exp(x)*x)

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maxima [A]  time = 0.39, size = 7, normalized size = 0.64 \begin {gather*} -e^{\left (x e^{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-e^(x*e^x)

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mupad [B]  time = 0.06, size = 7, normalized size = 0.64 \begin {gather*} -{\mathrm {e}}^{x\,{\mathrm {e}}^x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(x*exp(x))*exp(x)*(x + 1),x)

[Out]

-exp(x*exp(x))

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sympy [A]  time = 0.13, size = 7, normalized size = 0.64 \begin {gather*} - e^{x e^{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-exp(x*exp(x))

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