3.2.99 \(\int e^{2 e^{6+x} x+e^6 (4 x^2-4 x^3)} (e^{6+x} (2+2 x)+e^6 (8 x-12 x^2)) \, dx\)

Optimal. Leaf size=22 \[ e^{4 e^6 x \left (\frac {e^x}{2}+x-x^2\right )} \]

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Rubi [A]  time = 0.14, antiderivative size = 25, normalized size of antiderivative = 1.14, number of steps used = 1, number of rules used = 1, integrand size = 52, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {6706} \begin {gather*} e^{4 e^6 \left (x^2-x^3\right )+2 e^{x+6} x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^(2*E^(6 + x)*x + E^6*(4*x^2 - 4*x^3))*(E^(6 + x)*(2 + 2*x) + E^6*(8*x - 12*x^2)),x]

[Out]

E^(2*E^(6 + x)*x + 4*E^6*(x^2 - 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^{2 e^{6+x} x+4 e^6 \left (x^2-x^3\right )}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.29, size = 18, normalized size = 0.82 \begin {gather*} e^{2 e^6 x \left (e^x-2 (-1+x) x\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(2*E^(6 + x)*x + E^6*(4*x^2 - 4*x^3))*(E^(6 + x)*(2 + 2*x) + E^6*(8*x - 12*x^2)),x]

[Out]

E^(2*E^6*x*(E^x - 2*(-1 + x)*x))

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fricas [A]  time = 0.62, size = 22, normalized size = 1.00 \begin {gather*} e^{\left (-4 \, {\left (x^{3} - x^{2}\right )} e^{6} + 2 \, x e^{\left (x + 6\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x+2)*exp(6)*exp(x)+(-12*x^2+8*x)*exp(6))*exp(2*x*exp(6)*exp(x)+(-4*x^3+4*x^2)*exp(6)),x, algorit
hm="fricas")

[Out]

e^(-4*(x^3 - x^2)*e^6 + 2*x*e^(x + 6))

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giac [A]  time = 0.36, size = 23, normalized size = 1.05 \begin {gather*} e^{\left (-4 \, x^{3} e^{6} + 4 \, x^{2} e^{6} + 2 \, x e^{\left (x + 6\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x+2)*exp(6)*exp(x)+(-12*x^2+8*x)*exp(6))*exp(2*x*exp(6)*exp(x)+(-4*x^3+4*x^2)*exp(6)),x, algorit
hm="giac")

[Out]

e^(-4*x^3*e^6 + 4*x^2*e^6 + 2*x*e^(x + 6))

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maple [A]  time = 0.08, size = 24, normalized size = 1.09

method	result	size
norman	\({\mathrm e}^{2 x \,{\mathrm e}^{6} {\mathrm e}^{x}+\left (-4 x^{3}+4 x^{2}\right ) {\mathrm e}^{6}}\)	\(24\)
risch	\({\mathrm e}^{-2 x \left (2 x^{2} {\mathrm e}^{6}-2 x \,{\mathrm e}^{6}-{\mathrm e}^{x +6}\right )}\)	\(24\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((2*x+2)*exp(6)*exp(x)+(-12*x^2+8*x)*exp(6))*exp(2*x*exp(6)*exp(x)+(-4*x^3+4*x^2)*exp(6)),x,method=_RETURN
VERBOSE)

[Out]

exp(2*x*exp(6)*exp(x)+(-4*x^3+4*x^2)*exp(6))

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maxima [A]  time = 0.75, size = 23, normalized size = 1.05 \begin {gather*} e^{\left (-4 \, x^{3} e^{6} + 4 \, x^{2} e^{6} + 2 \, x e^{\left (x + 6\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x+2)*exp(6)*exp(x)+(-12*x^2+8*x)*exp(6))*exp(2*x*exp(6)*exp(x)+(-4*x^3+4*x^2)*exp(6)),x, algorit
hm="maxima")

[Out]

e^(-4*x^3*e^6 + 4*x^2*e^6 + 2*x*e^(x + 6))

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mupad [B]  time = 0.35, size = 25, normalized size = 1.14 \begin {gather*} {\mathrm {e}}^{4\,x^2\,{\mathrm {e}}^6}\,{\mathrm {e}}^{-4\,x^3\,{\mathrm {e}}^6}\,{\mathrm {e}}^{2\,x\,{\mathrm {e}}^6\,{\mathrm {e}}^x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(exp(6)*(4*x^2 - 4*x^3) + 2*x*exp(6)*exp(x))*(exp(6)*(8*x - 12*x^2) + exp(6)*exp(x)*(2*x + 2)),x)

[Out]

exp(4*x^2*exp(6))*exp(-4*x^3*exp(6))*exp(2*x*exp(6)*exp(x))

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sympy [A]  time = 0.22, size = 24, normalized size = 1.09 \begin {gather*} e^{2 x e^{6} e^{x} + \left (- 4 x^{3} + 4 x^{2}\right ) e^{6}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x+2)*exp(6)*exp(x)+(-12*x**2+8*x)*exp(6))*exp(2*x*exp(6)*exp(x)+(-4*x**3+4*x**2)*exp(6)),x)

[Out]

exp(2*x*exp(6)*exp(x) + (-4*x**3 + 4*x**2)*exp(6))

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