3.33.62 \(\int e^{2+x-8 e^x x} (-8-8 x) \, dx\) [3262]

Optimal. Leaf size=10 \[ e^{2-8 e^x x} \]

[Out]

exp(x)*exp(-8*exp(x)*x+2-x)

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Rubi [F]
time = 0.14, 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^{2+x-8 e^x x} (-8-8 x) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[E^(2 + x - 8*E^x*x)*(-8 - 8*x),x]

[Out]

-8*Defer[Int][E^(2 + x - 8*E^x*x), x] - 8*Defer[Int][E^(2 + x - 8*E^x*x)*x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-8 e^{2+x-8 e^x x}-8 e^{2+x-8 e^x x} x\right ) \, dx\\ &=-\left (8 \int e^{2+x-8 e^x x} \, dx\right )-8 \int e^{2+x-8 e^x x} x \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.03, size = 10, normalized size = 1.00 \begin {gather*} e^{2-8 e^x x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(2 + x - 8*E^x*x)*(-8 - 8*x),x]

[Out]

E^(2 - 8*E^x*x)

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Maple [A]
time = 0.32, size = 9, normalized size = 0.90

method	result	size
risch	\({\mathrm e}^{-8 \,{\mathrm e}^{x} x +2}\)	\(9\)
norman	\({\mathrm e}^{x} {\mathrm e}^{-8 \,{\mathrm e}^{x} x +2-x}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-8*x-8)*exp(x)^2*exp(-8*exp(x)*x+2-x),x,method=_RETURNVERBOSE)

[Out]

exp(-8*exp(x)*x+2)

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Maxima [A]
time = 0.30, size = 8, normalized size = 0.80 \begin {gather*} e^{\left (-8 \, x e^{x} + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-8*x-8)*exp(x)^2*exp(-8*exp(x)*x+2-x),x, algorithm="maxima")

[Out]

e^(-8*x*e^x + 2)

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Fricas [A]
time = 0.41, size = 8, normalized size = 0.80 \begin {gather*} e^{\left (-8 \, x e^{x} + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-8*x-8)*exp(x)^2*exp(-8*exp(x)*x+2-x),x, algorithm="fricas")

[Out]

e^(-8*x*e^x + 2)

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Sympy [A]
time = 0.07, size = 14, normalized size = 1.40 \begin {gather*} e^{x} e^{- 8 x e^{x} - x + 2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-8*x-8)*exp(x)**2*exp(-8*exp(x)*x+2-x),x)

[Out]

exp(x)*exp(-8*x*exp(x) - x + 2)

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Giac [A]
time = 0.40, size = 8, normalized size = 0.80 \begin {gather*} e^{\left (-8 \, x e^{x} + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-8*x-8)*exp(x)^2*exp(-8*exp(x)*x+2-x),x, algorithm="giac")

[Out]

e^(-8*x*e^x + 2)

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Mupad [B]
time = 0.07, size = 9, normalized size = 0.90 \begin {gather*} {\mathrm {e}}^{-8\,x\,{\mathrm {e}}^x}\,{\mathrm {e}}^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(2*x)*exp(2 - 8*x*exp(x) - x)*(8*x + 8),x)

[Out]

exp(-8*x*exp(x))*exp(2)

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