3.101.1 \(\int \frac {e^{\frac {e^{e^{x^2}-x-4 x^4}-x^4}{x}} (-3 x^4+e^{e^{x^2}-x-4 x^4} (-1-x+2 e^{x^2} x^2-16 x^4))}{x^2} \, dx\)

Optimal. Leaf size=28 \[ e^{\frac {e^{e^{x^2}-x-4 x^4}-x^4}{x}} \]

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Rubi [A]  time = 0.84, antiderivative size = 28, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 75, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.013, Rules used = {6706} \begin {gather*} e^{\frac {e^{-4 x^4+e^{x^2}-x}-x^4}{x}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E^((E^(E^x^2 - x - 4*x^4) - x^4)/x)*(-3*x^4 + E^(E^x^2 - x - 4*x^4)*(-1 - x + 2*E^x^2*x^2 - 16*x^4)))/x^2
,x]

[Out]

E^((E^(E^x^2 - x - 4*x^4) - x^4)/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^{\frac {e^{e^{x^2}-x-4 x^4}-x^4}{x}}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 2.65, size = 28, normalized size = 1.00 \begin {gather*} e^{\frac {e^{e^{x^2}-x-4 x^4}}{x}-x^3} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((E^(E^x^2 - x - 4*x^4) - x^4)/x)*(-3*x^4 + E^(E^x^2 - x - 4*x^4)*(-1 - x + 2*E^x^2*x^2 - 16*x^4)
))/x^2,x]

[Out]

E^(E^(E^x^2 - x - 4*x^4)/x - x^3)

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fricas [A]  time = 1.37, size = 26, normalized size = 0.93 \begin {gather*} e^{\left (-\frac {x^{4} - e^{\left (-4 \, x^{4} - x + e^{\left (x^{2}\right )}\right )}}{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^2*exp(x^2)-16*x^4-x-1)*exp(exp(x^2)-4*x^4-x)-3*x^4)*exp((exp(exp(x^2)-4*x^4-x)-x^4)/x)/x^2,x,
algorithm="fricas")

[Out]

e^(-(x^4 - e^(-4*x^4 - x + e^(x^2)))/x)

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giac [A]  time = 0.23, size = 25, normalized size = 0.89 \begin {gather*} e^{\left (-x^{3} + \frac {e^{\left (-4 \, x^{4} - x + e^{\left (x^{2}\right )}\right )}}{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^2*exp(x^2)-16*x^4-x-1)*exp(exp(x^2)-4*x^4-x)-3*x^4)*exp((exp(exp(x^2)-4*x^4-x)-x^4)/x)/x^2,x,
algorithm="giac")

[Out]

e^(-x^3 + e^(-4*x^4 - x + e^(x^2))/x)

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maple [A]  time = 0.06, size = 27, normalized size = 0.96

method	result	size
risch	\({\mathrm e}^{-\frac {-{\mathrm e}^{{\mathrm e}^{x^{2}}-4 x^{4}-x}+x^{4}}{x}}\)	\(27\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((2*x^2*exp(x^2)-16*x^4-x-1)*exp(exp(x^2)-4*x^4-x)-3*x^4)*exp((exp(exp(x^2)-4*x^4-x)-x^4)/x)/x^2,x,method=
_RETURNVERBOSE)

[Out]

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

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maxima [A]  time = 0.61, size = 25, normalized size = 0.89 \begin {gather*} e^{\left (-x^{3} + \frac {e^{\left (-4 \, x^{4} - x + e^{\left (x^{2}\right )}\right )}}{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^2*exp(x^2)-16*x^4-x-1)*exp(exp(x^2)-4*x^4-x)-3*x^4)*exp((exp(exp(x^2)-4*x^4-x)-x^4)/x)/x^2,x,
algorithm="maxima")

[Out]

e^(-x^3 + e^(-4*x^4 - x + e^(x^2))/x)

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mupad [B]  time = 6.62, size = 27, normalized size = 0.96 \begin {gather*} {\mathrm {e}}^{\frac {{\mathrm {e}}^{-x}\,{\mathrm {e}}^{-4\,x^4}\,{\mathrm {e}}^{{\mathrm {e}}^{x^2}}}{x}}\,{\mathrm {e}}^{-x^3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp((exp(exp(x^2) - x - 4*x^4) - x^4)/x)*(3*x^4 + exp(exp(x^2) - x - 4*x^4)*(x - 2*x^2*exp(x^2) + 16*x^4
+ 1)))/x^2,x)

[Out]

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

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sympy [A]  time = 0.88, size = 19, normalized size = 0.68 \begin {gather*} e^{\frac {- x^{4} + e^{- 4 x^{4} - x + e^{x^{2}}}}{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x**2*exp(x**2)-16*x**4-x-1)*exp(exp(x**2)-4*x**4-x)-3*x**4)*exp((exp(exp(x**2)-4*x**4-x)-x**4)/x
)/x**2,x)

[Out]

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

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