3.33.62 $\int e^{2+x-8e^{x}x}(-8-8x)dx$

Optimal. Leaf size=10 $$e^{2-8e^{x}x}$$

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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 = {} $$\begin{array}{c}\int e^{2+x-8e^{x}x}(-8-8x)dx\end{array}$$

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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int (-8e^{2+x-8e^{x}x}-8e^{2+x-8e^{x}x}x)dx\\ & =-(8\int e^{2+x-8e^{x}x}dx)-8\int e^{2+x-8e^{x}x}xdx\end{array}\end{array}$$

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Mathematica [A]  time = 0.06, size = 10, normalized size = 1.00 $$\begin{array}{c}{e}^{2-8e^{x}x}\end{array}$$

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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fricas [A]  time = 0.56, size = 8, normalized size = 0.80 $$\begin{array}{c}{e}^{(-8x{e}^x+2)}\end{array}$$

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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giac [A]  time = 0.23, size = 8, normalized size = 0.80 $$\begin{array}{c}{e}^{(-8x{e}^x+2)}\end{array}$$

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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maple [A]  time = 0.06, 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 = 0.60, size = 8, normalized size = 0.80 $$\begin{array}{c}{e}^{(-8x{e}^x+2)}\end{array}$$

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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mupad [B]  time = 0.07, size = 9, normalized size = 0.90 $$\begin{array}{c}{\mathrm{e}}^{-8x{\mathrm{e}}^x}{\mathrm{e}}^2\end{array}$$

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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sympy [A]  time = 0.17, size = 14, normalized size = 1.40 $$\begin{array}{c}{e}^x{e}^{-8x{e}^x-x+2}\end{array}$$

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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