3.51.14 \(\int e^{-9-e^x} x (12 x-4 e^x x^2) \, dx\)

Optimal. Leaf size=14 \[ 4 e^{-9-e^x} x^3 \]

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Rubi [A]  time = 0.03, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {2288} \begin {gather*} 4 e^{-e^x-9} x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^(-9 - E^x)*x*(12*x - 4*E^x*x^2),x]

[Out]

4*E^(-9 - E^x)*x^3

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} &=4 e^{-9-e^x} x^3\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 14, normalized size = 1.00 \begin {gather*} 4 e^{-9-e^x} x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(-9 - E^x)*x*(12*x - 4*E^x*x^2),x]

[Out]

4*E^(-9 - E^x)*x^3

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fricas [A]  time = 0.91, size = 14, normalized size = 1.00 \begin {gather*} 4 \, x^{2} e^{\left (-e^{x} + \log \relax (x) - 9\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*exp(x)*x^2+12*x)*exp(log(x)-9)/exp(exp(x)),x, algorithm="fricas")

[Out]

4*x^2*e^(-e^x + log(x) - 9)

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giac [A]  time = 0.14, size = 12, normalized size = 0.86 \begin {gather*} 4 \, x^{3} e^{\left (-e^{x} - 9\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*exp(x)*x^2+12*x)*exp(log(x)-9)/exp(exp(x)),x, algorithm="giac")

[Out]

4*x^3*e^(-e^x - 9)

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maple [A]  time = 0.10, size = 13, normalized size = 0.93

method	result	size
risch	\(4 x^{3} {\mathrm e}^{-{\mathrm e}^{x}-9}\)	\(13\)
norman	\(4 \,{\mathrm e}^{-9} x^{3} {\mathrm e}^{-{\mathrm e}^{x}}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-4*exp(x)*x^2+12*x)*exp(ln(x)-9)/exp(exp(x)),x,method=_RETURNVERBOSE)

[Out]

4*x^3*exp(-exp(x)-9)

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maxima [A]  time = 0.42, size = 12, normalized size = 0.86 \begin {gather*} 4 \, x^{3} e^{\left (-e^{x} - 9\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*exp(x)*x^2+12*x)*exp(log(x)-9)/exp(exp(x)),x, algorithm="maxima")

[Out]

4*x^3*e^(-e^x - 9)

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mupad [B]  time = 3.35, size = 12, normalized size = 0.86 \begin {gather*} 4\,x^3\,{\mathrm {e}}^{-9}\,{\mathrm {e}}^{-{\mathrm {e}}^x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(-exp(x))*exp(log(x) - 9)*(12*x - 4*x^2*exp(x)),x)

[Out]

4*x^3*exp(-9)*exp(-exp(x))

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sympy [A]  time = 0.16, size = 12, normalized size = 0.86 \begin {gather*} \frac {4 x^{3} e^{- e^{x}}}{e^{9}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*exp(x)*x**2+12*x)*exp(ln(x)-9)/exp(exp(x)),x)

[Out]

4*x**3*exp(-9)*exp(-exp(x))

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