3.39.4 \(\int e^{-16-14 x+2 x^2-2 e^x x^3} (-14+4 x+e^x (-6 x^2-2 x^3)) \, dx\)

Optimal. Leaf size=20 \[ e^{-16-14 x+2 x^2-2 e^x x^3} \]

________________________________________________________________________________________

Rubi [A]  time = 0.13, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 41, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {6706} \begin {gather*} e^{-2 e^x x^3+2 x^2-14 x-16} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^(-16 - 14*x + 2*x^2 - 2*E^x*x^3)*(-14 + 4*x + E^x*(-6*x^2 - 2*x^3)),x]

[Out]

E^(-16 - 14*x + 2*x^2 - 2*E^x*x^3)

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^{-16-14 x+2 x^2-2 e^x x^3}\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.37, size = 20, normalized size = 1.00 \begin {gather*} e^{-16-14 x+2 x^2-2 e^x x^3} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(-16 - 14*x + 2*x^2 - 2*E^x*x^3)*(-14 + 4*x + E^x*(-6*x^2 - 2*x^3)),x]

[Out]

E^(-16 - 14*x + 2*x^2 - 2*E^x*x^3)

________________________________________________________________________________________

fricas [A]  time = 0.65, size = 18, normalized size = 0.90 \begin {gather*} e^{\left (-2 \, x^{3} e^{x} + 2 \, x^{2} - 14 \, x - 16\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x^3-6*x^2)*exp(x)+4*x-14)*exp(-exp(x)*x^3+x^2-7*x-8)^2,x, algorithm="fricas")

[Out]

e^(-2*x^3*e^x + 2*x^2 - 14*x - 16)

________________________________________________________________________________________

giac [A]  time = 0.23, size = 18, normalized size = 0.90 \begin {gather*} e^{\left (-2 \, x^{3} e^{x} + 2 \, x^{2} - 14 \, x - 16\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x^3-6*x^2)*exp(x)+4*x-14)*exp(-exp(x)*x^3+x^2-7*x-8)^2,x, algorithm="giac")

[Out]

e^(-2*x^3*e^x + 2*x^2 - 14*x - 16)

________________________________________________________________________________________

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

method	result	size
norman	\({\mathrm e}^{-2 \,{\mathrm e}^{x} x^{3}+2 x^{2}-14 x -16}\)	\(19\)
risch	\({\mathrm e}^{-2 \,{\mathrm e}^{x} x^{3}+2 x^{2}-14 x -16}\)	\(19\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-2*x^3-6*x^2)*exp(x)+4*x-14)*exp(-exp(x)*x^3+x^2-7*x-8)^2,x,method=_RETURNVERBOSE)

[Out]

exp(-exp(x)*x^3+x^2-7*x-8)^2

________________________________________________________________________________________

maxima [A]  time = 0.54, size = 18, normalized size = 0.90 \begin {gather*} e^{\left (-2 \, x^{3} e^{x} + 2 \, x^{2} - 14 \, x - 16\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x^3-6*x^2)*exp(x)+4*x-14)*exp(-exp(x)*x^3+x^2-7*x-8)^2,x, algorithm="maxima")

[Out]

e^(-2*x^3*e^x + 2*x^2 - 14*x - 16)

________________________________________________________________________________________

mupad [B]  time = 0.09, size = 21, normalized size = 1.05 \begin {gather*} {\mathrm {e}}^{-14\,x}\,{\mathrm {e}}^{-16}\,{\mathrm {e}}^{-2\,x^3\,{\mathrm {e}}^x}\,{\mathrm {e}}^{2\,x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(2*x^2 - 2*x^3*exp(x) - 14*x - 16)*(exp(x)*(6*x^2 + 2*x^3) - 4*x + 14),x)

[Out]

exp(-14*x)*exp(-16)*exp(-2*x^3*exp(x))*exp(2*x^2)

________________________________________________________________________________________

sympy [A]  time = 0.20, size = 19, normalized size = 0.95 \begin {gather*} e^{- 2 x^{3} e^{x} + 2 x^{2} - 14 x - 16} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x**3-6*x**2)*exp(x)+4*x-14)*exp(-exp(x)*x**3+x**2-7*x-8)**2,x)

[Out]

exp(-2*x**3*exp(x) + 2*x**2 - 14*x - 16)

________________________________________________________________________________________