3.46.73 \(\int e^{-e^{2 e^{-x} x}} (3 e^x+e^{2 e^{-x} x} (-6+6 x)) \, dx\)

Optimal. Leaf size=20 \[ -1+3 e^{-e^{2 e^{-x} x}+x} \]

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Rubi [A]  time = 0.04, antiderivative size = 37, normalized size of antiderivative = 1.85, number of steps used = 1, number of rules used = 1, integrand size = 37, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.027, Rules used = {2288} \begin {gather*} \frac {3 e^{-e^{2 e^{-x} x}} (1-x)}{e^{-x}-e^{-x} x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(3*E^x + E^((2*x)/E^x)*(-6 + 6*x))/E^E^((2*x)/E^x),x]

[Out]

(3*(1 - x))/(E^E^((2*x)/E^x)*(E^(-x) - x/E^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} &=\frac {3 e^{-e^{2 e^{-x} x}} (1-x)}{e^{-x}-e^{-x} x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.03, size = 18, normalized size = 0.90 \begin {gather*} 3 e^{-e^{2 e^{-x} x}+x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(3*E^x + E^((2*x)/E^x)*(-6 + 6*x))/E^E^((2*x)/E^x),x]

[Out]

3*E^(-E^((2*x)/E^x) + x)

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fricas [A]  time = 0.55, size = 15, normalized size = 0.75 \begin {gather*} 3 \, e^{\left (x - e^{\left (2 \, x e^{\left (-x\right )}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((6*x-6)*exp(2*x/exp(x))+3*exp(x))/exp(exp(2*x/exp(x))),x, algorithm="fricas")

[Out]

3*e^(x - e^(2*x*e^(-x)))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int 3 \, {\left (2 \, {\left (x - 1\right )} e^{\left (2 \, x e^{\left (-x\right )}\right )} + e^{x}\right )} e^{\left (-e^{\left (2 \, x e^{\left (-x\right )}\right )}\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((6*x-6)*exp(2*x/exp(x))+3*exp(x))/exp(exp(2*x/exp(x))),x, algorithm="giac")

[Out]

integrate(3*(2*(x - 1)*e^(2*x*e^(-x)) + e^x)*e^(-e^(2*x*e^(-x))), x)

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maple [A]  time = 0.05, size = 16, normalized size = 0.80

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((6*x-6)*exp(2*x/exp(x))+3*exp(x))/exp(exp(2*x/exp(x))),x,method=_RETURNVERBOSE)

[Out]

3*exp(x)/exp(exp(2*x/exp(x)))

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maxima [A]  time = 0.42, size = 15, normalized size = 0.75 \begin {gather*} 3 \, e^{\left (x - e^{\left (2 \, x e^{\left (-x\right )}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((6*x-6)*exp(2*x/exp(x))+3*exp(x))/exp(exp(2*x/exp(x))),x, algorithm="maxima")

[Out]

3*e^(x - e^(2*x*e^(-x)))

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mupad [B]  time = 3.13, size = 15, normalized size = 0.75 \begin {gather*} 3\,{\mathrm {e}}^{-{\mathrm {e}}^{2\,x\,{\mathrm {e}}^{-x}}}\,{\mathrm {e}}^x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(-exp(2*x*exp(-x)))*(3*exp(x) + exp(2*x*exp(-x))*(6*x - 6)),x)

[Out]

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

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sympy [A]  time = 0.27, size = 14, normalized size = 0.70 \begin {gather*} 3 e^{x} e^{- e^{2 x e^{- x}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((6*x-6)*exp(2*x/exp(x))+3*exp(x))/exp(exp(2*x/exp(x))),x)

[Out]

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

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