3.98.33 \(\int e^{4 e^{-2 x^3}} (e^{12}-24 e^{12-2 x^3} x^3) \, dx\)

Optimal. Leaf size=15 \[ e^{12+4 e^{-2 x^3}} x \]

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Rubi [A]  time = 0.03, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.033, Rules used = {2288} \begin {gather*} e^{4 e^{-2 x^3}+12} x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^(4/E^(2*x^3))*(E^12 - 24*E^(12 - 2*x^3)*x^3),x]

[Out]

E^(12 + 4/E^(2*x^3))*x

Rule 2288

Int[(y_.)*(F_)^(u_)*((v_) + (w_)), x_Symbol] :> With[{z = (v*y)/(Log[F]*D[u, x])}, Simp[F^u*z, x] /; EqQ[D[z,
x], w*y]] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=e^{12+4 e^{-2 x^3}} x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.10, size = 15, normalized size = 1.00 \begin {gather*} e^{4 \left (3+e^{-2 x^3}\right )} x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(4/E^(2*x^3))*(E^12 - 24*E^(12 - 2*x^3)*x^3),x]

[Out]

E^(4*(3 + E^(-2*x^3)))*x

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fricas [A]  time = 0.58, size = 13, normalized size = 0.87 \begin {gather*} x e^{\left (4 \, e^{\left (-2 \, x^{3}\right )} + 12\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-24*x^3*exp(3)^4*exp(-x^3)^2+exp(3)^4)*exp(exp(-x^3)^2)^4,x, algorithm="fricas")

[Out]

x*e^(4*e^(-2*x^3) + 12)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -{\left (24 \, x^{3} e^{\left (-2 \, x^{3} + 12\right )} - e^{12}\right )} e^{\left (4 \, e^{\left (-2 \, x^{3}\right )}\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-24*x^3*exp(3)^4*exp(-x^3)^2+exp(3)^4)*exp(exp(-x^3)^2)^4,x, algorithm="giac")

[Out]

integrate(-(24*x^3*e^(-2*x^3 + 12) - e^12)*e^(4*e^(-2*x^3)), x)

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maple [A]  time = 0.05, size = 14, normalized size = 0.93

method	result	size
risch	\(x \,{\mathrm e}^{4 \,{\mathrm e}^{-2 x^{3}}+12}\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-24*x^3*exp(3)^4*exp(-x^3)^2+exp(3)^4)*exp(exp(-x^3)^2)^4,x,method=_RETURNVERBOSE)

[Out]

x*exp(4*exp(-2*x^3)+12)

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -\int {\left (24 \, x^{3} e^{\left (-2 \, x^{3} + 12\right )} - e^{12}\right )} e^{\left (4 \, e^{\left (-2 \, x^{3}\right )}\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-24*x^3*exp(3)^4*exp(-x^3)^2+exp(3)^4)*exp(exp(-x^3)^2)^4,x, algorithm="maxima")

[Out]

-integrate((24*x^3*e^(-2*x^3 + 12) - e^12)*e^(4*e^(-2*x^3)), x)

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mupad [B]  time = 5.77, size = 13, normalized size = 0.87 \begin {gather*} x\,{\mathrm {e}}^{4\,{\mathrm {e}}^{-2\,x^3}}\,{\mathrm {e}}^{12} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(4*exp(-2*x^3))*(exp(12) - 24*x^3*exp(12)*exp(-2*x^3)),x)

[Out]

x*exp(4*exp(-2*x^3))*exp(12)

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sympy [A]  time = 0.85, size = 14, normalized size = 0.93 \begin {gather*} x e^{12} e^{4 e^{- 2 x^{3}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-24*x**3*exp(3)**4*exp(-x**3)**2+exp(3)**4)*exp(exp(-x**3)**2)**4,x)

[Out]

x*exp(12)*exp(4*exp(-2*x**3))

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