3.39.32 \(\int 12 e^{1-e^3} x^2 \, dx\)

Optimal. Leaf size=14 \[ 4 e^{1-e^3} x^3 \]

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Rubi [A]  time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 30} \begin {gather*} 4 e^{1-e^3} x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[12*E^(1 - E^3)*x^2,x]

[Out]

4*E^(1 - E^3)*x^3

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\left (12 e^{1-e^3}\right ) \int x^2 \, dx\\ &=4 e^{1-e^3} x^3\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} 4 e^{1-e^3} x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[12*E^(1 - E^3)*x^2,x]

[Out]

4*E^(1 - E^3)*x^3

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fricas [A]  time = 0.62, size = 12, normalized size = 0.86 \begin {gather*} 4 \, x^{3} e^{\left (-e^{3} + 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

4*x^3*e^(-e^3 + 1)

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giac [A]  time = 0.13, size = 12, normalized size = 0.86 \begin {gather*} 4 \, x^{3} e^{\left (-e^{3} + 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

4*x^3*e^(-e^3 + 1)

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maple [A]  time = 0.03, size = 13, normalized size = 0.93

method	result	size
default	\(4 \,{\mathrm e} \,{\mathrm e}^{-{\mathrm e}^{3}} x^{3}\)	\(13\)
norman	\(4 \,{\mathrm e} \,{\mathrm e}^{-{\mathrm e}^{3}} x^{3}\)	\(13\)
risch	\(4 x^{3} {\mathrm e}^{-{\mathrm e}^{3}+1}\)	\(13\)
gosper	\(4 \,{\mathrm e} \,{\mathrm e}^{-{\mathrm e}^{3}} x^{3}\)	\(20\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(12*x^2*exp(1)/exp(exp(3-x)*exp(x)),x,method=_RETURNVERBOSE)

[Out]

4*exp(1)*x^3/exp(exp(3))

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maxima [A]  time = 0.34, size = 12, normalized size = 0.86 \begin {gather*} 4 \, x^{3} e^{\left (-e^{3} + 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

4*x^3*e^(-e^3 + 1)

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mupad [B]  time = 0.04, size = 12, normalized size = 0.86 \begin {gather*} 4\,x^3\,{\mathrm {e}}^{1-{\mathrm {e}}^3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

4*x^3*exp(1 - exp(3))

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sympy [A]  time = 0.06, size = 12, normalized size = 0.86 \begin {gather*} \frac {4 e x^{3}}{e^{e^{3}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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