3.46.3 \(\int e^{e^{4-6 x+6 x^2}-x} (-e^2+e^{6-6 x+6 x^2} (-6+12 x)) \, dx\)

Optimal. Leaf size=19 \[ e^{2+e^{4-6 x+6 x^2}-x} \]

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Rubi [A]  time = 0.13, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 43, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.023, Rules used = {6706} \begin {gather*} e^{e^{6 x^2-6 x+4}-x+2} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^(E^(4 - 6*x + 6*x^2) - x)*(-E^2 + E^(6 - 6*x + 6*x^2)*(-6 + 12*x)),x]

[Out]

E^(2 + E^(4 - 6*x + 6*x^2) - 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} &=e^{2+e^{4-6 x+6 x^2}-x}\\ \end {aligned} \end {gather*}

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Mathematica [F]  time = 0.43, size = 0, normalized size = 0.00 \begin {gather*} \int e^{e^{4-6 x+6 x^2}-x} \left (-e^2+e^{6-6 x+6 x^2} (-6+12 x)\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[E^(E^(4 - 6*x + 6*x^2) - x)*(-E^2 + E^(6 - 6*x + 6*x^2)*(-6 + 12*x)),x]

[Out]

Integrate[E^(E^(4 - 6*x + 6*x^2) - x)*(-E^2 + E^(6 - 6*x + 6*x^2)*(-6 + 12*x)), x]

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fricas [A]  time = 0.55, size = 25, normalized size = 1.32 \begin {gather*} e^{\left (-{\left (x e^{2} - e^{\left (6 \, x^{2} - 6 \, x + 6\right )}\right )} e^{\left (-2\right )} + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((12*x-6)*exp(2)*exp(3*x^2-3*x+2)^2-exp(2))*exp(exp(3*x^2-3*x+2)^2-x),x, algorithm="fricas")

[Out]

e^(-(x*e^2 - e^(6*x^2 - 6*x + 6))*e^(-2) + 2)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int {\left (6 \, {\left (2 \, x - 1\right )} e^{\left (6 \, x^{2} - 6 \, x + 6\right )} - e^{2}\right )} e^{\left (-x + e^{\left (6 \, x^{2} - 6 \, x + 4\right )}\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((12*x-6)*exp(2)*exp(3*x^2-3*x+2)^2-exp(2))*exp(exp(3*x^2-3*x+2)^2-x),x, algorithm="giac")

[Out]

integrate((6*(2*x - 1)*e^(6*x^2 - 6*x + 6) - e^2)*e^(-x + e^(6*x^2 - 6*x + 4)), x)

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maple [A]  time = 0.08, size = 18, normalized size = 0.95

method	result	size
risch	\({\mathrm e}^{2+{\mathrm e}^{6 x^{2}-6 x +4}-x}\)	\(18\)
norman	\({\mathrm e}^{2} {\mathrm e}^{{\mathrm e}^{6 x^{2}-6 x +4}-x}\)	\(22\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((12*x-6)*exp(2)*exp(3*x^2-3*x+2)^2-exp(2))*exp(exp(3*x^2-3*x+2)^2-x),x,method=_RETURNVERBOSE)

[Out]

exp(2+exp(6*x^2-6*x+4)-x)

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maxima [A]  time = 0.59, size = 17, normalized size = 0.89 \begin {gather*} e^{\left (-x + e^{\left (6 \, x^{2} - 6 \, x + 4\right )} + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((12*x-6)*exp(2)*exp(3*x^2-3*x+2)^2-exp(2))*exp(exp(3*x^2-3*x+2)^2-x),x, algorithm="maxima")

[Out]

e^(-x + e^(6*x^2 - 6*x + 4) + 2)

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mupad [B]  time = 0.13, size = 21, normalized size = 1.11 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{-6\,x}\,{\mathrm {e}}^4\,{\mathrm {e}}^{6\,x^2}}\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(exp(6*x^2 - 6*x + 4) - x)*(exp(2) - exp(2)*exp(6*x^2 - 6*x + 4)*(12*x - 6)),x)

[Out]

exp(exp(-6*x)*exp(4)*exp(6*x^2))*exp(-x)*exp(2)

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sympy [A]  time = 0.36, size = 17, normalized size = 0.89 \begin {gather*} e^{2} e^{- x + e^{6 x^{2} - 6 x + 4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((12*x-6)*exp(2)*exp(3*x**2-3*x+2)**2-exp(2))*exp(exp(3*x**2-3*x+2)**2-x),x)

[Out]

exp(2)*exp(-x + exp(6*x**2 - 6*x + 4))

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