3.23.54 \(\int e^{-3 e^{-2+2 x+x^2}+8 x} (16+e^{-2+2 x+x^2} (-12-12 x)) \, dx\)

Optimal. Leaf size=20 \[ 2 e^{-3 e^{-2+2 x+x^2}+8 x} \]

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Rubi [A]  time = 0.14, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 37, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.027, Rules used = {6706} \begin {gather*} 2 e^{8 x-3 e^{x^2+2 x-2}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^(-3*E^(-2 + 2*x + x^2) + 8*x)*(16 + E^(-2 + 2*x + x^2)*(-12 - 12*x)),x]

[Out]

2*E^(-3*E^(-2 + 2*x + x^2) + 8*x)

Rule 6706

Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Simp[(q*F^v)/Log[F], x] /;  !FalseQ[q]
] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=2 e^{-3 e^{-2+2 x+x^2}+8 x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.27, size = 20, normalized size = 1.00 \begin {gather*} 2 e^{-3 e^{-2+2 x+x^2}+8 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(-3*E^(-2 + 2*x + x^2) + 8*x)*(16 + E^(-2 + 2*x + x^2)*(-12 - 12*x)),x]

[Out]

2*E^(-3*E^(-2 + 2*x + x^2) + 8*x)

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fricas [A]  time = 0.94, size = 18, normalized size = 0.90 \begin {gather*} 2 \, e^{\left (8 \, x - 3 \, e^{\left (x^{2} + 2 \, x - 2\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-12*x-12)*exp(x^2+2*x-2)+16)*exp(-3*exp(x^2+2*x-2)+8*x),x, algorithm="fricas")

[Out]

2*e^(8*x - 3*e^(x^2 + 2*x - 2))

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giac [A]  time = 0.66, size = 18, normalized size = 0.90 \begin {gather*} 2 \, e^{\left (8 \, x - 3 \, e^{\left (x^{2} + 2 \, x - 2\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-12*x-12)*exp(x^2+2*x-2)+16)*exp(-3*exp(x^2+2*x-2)+8*x),x, algorithm="giac")

[Out]

2*e^(8*x - 3*e^(x^2 + 2*x - 2))

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maple [A]  time = 0.05, size = 19, normalized size = 0.95

method	result	size
norman	\(2 \,{\mathrm e}^{-3 \,{\mathrm e}^{x^{2}+2 x -2}+8 x}\)	\(19\)
risch	\(2 \,{\mathrm e}^{-3 \,{\mathrm e}^{x^{2}+2 x -2}+8 x}\)	\(19\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-12*x-12)*exp(x^2+2*x-2)+16)*exp(-3*exp(x^2+2*x-2)+8*x),x,method=_RETURNVERBOSE)

[Out]

2*exp(-3*exp(x^2+2*x-2)+8*x)

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maxima [A]  time = 0.67, size = 18, normalized size = 0.90 \begin {gather*} 2 \, e^{\left (8 \, x - 3 \, e^{\left (x^{2} + 2 \, x - 2\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-12*x-12)*exp(x^2+2*x-2)+16)*exp(-3*exp(x^2+2*x-2)+8*x),x, algorithm="maxima")

[Out]

2*e^(8*x - 3*e^(x^2 + 2*x - 2))

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mupad [B]  time = 1.29, size = 19, normalized size = 0.95 \begin {gather*} 2\,{\mathrm {e}}^{8\,x}\,{\mathrm {e}}^{-3\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{-2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(8*x - 3*exp(2*x + x^2 - 2))*(exp(2*x + x^2 - 2)*(12*x + 12) - 16),x)

[Out]

2*exp(8*x)*exp(-3*exp(2*x)*exp(x^2)*exp(-2))

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sympy [A]  time = 0.33, size = 17, normalized size = 0.85 \begin {gather*} 2 e^{8 x - 3 e^{x^{2} + 2 x - 2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-12*x-12)*exp(x**2+2*x-2)+16)*exp(-3*exp(x**2+2*x-2)+8*x),x)

[Out]

2*exp(8*x - 3*exp(x**2 + 2*x - 2))

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