3.30.71 $\int e^{4x+e^{2e^{4-3x^2}{x}^2}x}(4+e^{2e^{4-3x^2}{x}^2}(1+e^{4-3x^2}(4x^2-12x^4)))dx$

Optimal. Leaf size=22 $$e^{(4+e^{2e^{4-3x^2}{x}^2})x}$$

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Rubi [A]  time = 0.34, antiderivative size = 24, normalized size of antiderivative = 1.09, number of steps used = 1, number of rules used = 1, integrand size = 67, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.015, Rules used = {6706} $$\begin{array}{c}{e}^{e^{2e^{4-3x^2}{x}^2}x+4x}\end{array}$$

Antiderivative was successfully verified.

[In]

Int[E^(4*x + E^(2*E^(4 - 3*x^2)*x^2)*x)*(4 + E^(2*E^(4 - 3*x^2)*x^2)*(1 + E^(4 - 3*x^2)*(4*x^2 - 12*x^4))),x]

[Out]

E^(4*x + E^(2*E^(4 - 3*x^2)*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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =e^{4x+e^{2e^{4-3x^2}{x}^2}x}\end{array}\end{array}$$

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Mathematica [A]  time = 1.68, size = 24, normalized size = 1.09 $$\begin{array}{c}{e}^{4x+e^{2e^{4-3x^2}{x}^2}x}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[E^(4*x + E^(2*E^(4 - 3*x^2)*x^2)*x)*(4 + E^(2*E^(4 - 3*x^2)*x^2)*(1 + E^(4 - 3*x^2)*(4*x^2 - 12*x^4)
)),x]

[Out]

E^(4*x + E^(2*E^(4 - 3*x^2)*x^2)*x)

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fricas [A]  time = 0.67, size = 21, normalized size = 0.95 $$\begin{array}{c}{e}^{(x{e}^{\left(2x^2{e}^{(-3x^2+4)}\right)}+4x)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-12*x^4+4*x^2)*exp(-3*x^2+4)+1)*exp(2*x^2*exp(-3*x^2+4))+4)*exp(x*exp(2*x^2*exp(-3*x^2+4))+4*x),x
, algorithm="fricas")

[Out]

e^(x*e^(2*x^2*e^(-3*x^2 + 4)) + 4*x)

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giac [A]  time = 0.37, size = 21, normalized size = 0.95 $$\begin{array}{c}{e}^{(x{e}^{\left(2x^2{e}^{(-3x^2+4)}\right)}+4x)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-12*x^4+4*x^2)*exp(-3*x^2+4)+1)*exp(2*x^2*exp(-3*x^2+4))+4)*exp(x*exp(2*x^2*exp(-3*x^2+4))+4*x),x
, algorithm="giac")

[Out]

e^(x*e^(2*x^2*e^(-3*x^2 + 4)) + 4*x)

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maple [A]  time = 0.06, size = 20, normalized size = 0.91

method	result	size
risch	${\mathrm{e}}^{({\mathrm{e}}^{2x^2{\mathrm{e}}^{-3x^2+4}}+4)x}$	$20$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-12*x^4+4*x^2)*exp(-3*x^2+4)+1)*exp(2*x^2*exp(-3*x^2+4))+4)*exp(x*exp(2*x^2*exp(-3*x^2+4))+4*x),x,metho
d=_RETURNVERBOSE)

[Out]

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

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maxima [A]  time = 0.49, size = 21, normalized size = 0.95 $$\begin{array}{c}{e}^{(x{e}^{\left(2x^2{e}^{(-3x^2+4)}\right)}+4x)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-12*x^4+4*x^2)*exp(-3*x^2+4)+1)*exp(2*x^2*exp(-3*x^2+4))+4)*exp(x*exp(2*x^2*exp(-3*x^2+4))+4*x),x
, algorithm="maxima")

[Out]

e^(x*e^(2*x^2*e^(-3*x^2 + 4)) + 4*x)

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mupad [B]  time = 1.90, size = 22, normalized size = 1.00 $$\begin{array}{c}{\mathrm{e}}^{4x}{\mathrm{e}}^{x{\mathrm{e}}^{2x^2{\mathrm{e}}^4{\mathrm{e}}^{-3x^2}}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(4*x + x*exp(2*x^2*exp(4 - 3*x^2)))*(exp(2*x^2*exp(4 - 3*x^2))*(exp(4 - 3*x^2)*(4*x^2 - 12*x^4) + 1) +
4),x)

[Out]

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

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sympy [A]  time = 5.96, size = 20, normalized size = 0.91 $$\begin{array}{c}{e}^{x{e}^{2x^2{e}^{4-3x^2}}+4x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-12*x**4+4*x**2)*exp(-3*x**2+4)+1)*exp(2*x**2*exp(-3*x**2+4))+4)*exp(x*exp(2*x**2*exp(-3*x**2+4))
+4*x),x)

[Out]

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

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