3.55.62 \(\int -12 e^{34-6 x^2} x \, dx\)

Optimal. Leaf size=13 \[ e^{4+6 \left (5-x^2\right )} \]

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Rubi [A]  time = 0.01, antiderivative size = 9, normalized size of antiderivative = 0.69, number of steps used = 2, number of rules used = 2, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {12, 2209} \begin {gather*} e^{34-6 x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-12*E^(34 - 6*x^2)*x,x]

[Out]

E^(34 - 6*x^2)

Rule 12

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

Rule 2209

Int[(F_)^((a_.) + (b_.)*((c_.) + (d_.)*(x_))^(n_))*((e_.) + (f_.)*(x_))^(m_.), x_Symbol] :> Simp[((e + f*x)^n*
F^(a + b*(c + d*x)^n))/(b*f*n*(c + d*x)^n*Log[F]), x] /; FreeQ[{F, a, b, c, d, e, f, n}, x] && EqQ[m, n - 1] &
& EqQ[d*e - c*f, 0]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\left (12 \int e^{34-6 x^2} x \, dx\right )\\ &=e^{34-6 x^2}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 0.69 \begin {gather*} e^{34-6 x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-12*E^(34 - 6*x^2)*x,x]

[Out]

E^(34 - 6*x^2)

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fricas [A]  time = 0.57, size = 8, normalized size = 0.62 \begin {gather*} e^{\left (-6 \, x^{2} + 34\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-12*x*exp(-6*x^2+34),x, algorithm="fricas")

[Out]

e^(-6*x^2 + 34)

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giac [A]  time = 0.14, size = 8, normalized size = 0.62 \begin {gather*} e^{\left (-6 \, x^{2} + 34\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-12*x*exp(-6*x^2+34),x, algorithm="giac")

[Out]

e^(-6*x^2 + 34)

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maple [A]  time = 0.02, size = 9, normalized size = 0.69

method	result	size
gosper	\({\mathrm e}^{-6 x^{2}+34}\)	\(9\)
derivativedivides	\({\mathrm e}^{-6 x^{2}+34}\)	\(9\)
default	\({\mathrm e}^{-6 x^{2}+34}\)	\(9\)
norman	\({\mathrm e}^{-6 x^{2}+34}\)	\(9\)
risch	\({\mathrm e}^{-6 x^{2}+34}\)	\(9\)
meijerg	\(-{\mathrm e}^{34} \left (1-{\mathrm e}^{-6 x^{2}}\right )\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-12*x*exp(-6*x^2+34),x,method=_RETURNVERBOSE)

[Out]

exp(-6*x^2+34)

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maxima [A]  time = 0.36, size = 8, normalized size = 0.62 \begin {gather*} e^{\left (-6 \, x^{2} + 34\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-12*x*exp(-6*x^2+34),x, algorithm="maxima")

[Out]

e^(-6*x^2 + 34)

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mupad [B]  time = 3.39, size = 9, normalized size = 0.69 \begin {gather*} {\mathrm {e}}^{34}\,{\mathrm {e}}^{-6\,x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-12*x*exp(34 - 6*x^2),x)

[Out]

exp(34)*exp(-6*x^2)

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sympy [A]  time = 0.07, size = 7, normalized size = 0.54 \begin {gather*} e^{34 - 6 x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-12*x*exp(-6*x**2+34),x)

[Out]

exp(34 - 6*x**2)

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