3.36.1 \(\int -72 e^{135-9 x^2} x \, dx\)

Optimal. Leaf size=11 \[ 4 e^{-9 \left (-15+x^2\right )} \]

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Rubi [A]  time = 0.01, antiderivative size = 11, normalized size of antiderivative = 1.00, 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*} 4 e^{135-9 x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-72*E^(135 - 9*x^2)*x,x]

[Out]

4*E^(135 - 9*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 (72 \int e^{135-9 x^2} x \, dx\right )\\ &=4 e^{135-9 x^2}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} 4 e^{135-9 x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-72*E^(135 - 9*x^2)*x,x]

[Out]

4*E^(135 - 9*x^2)

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fricas [A]  time = 0.51, size = 10, normalized size = 0.91 \begin {gather*} 4 \, e^{\left (-9 \, x^{2} + 135\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-72*x/exp(9*x^2-135),x, algorithm="fricas")

[Out]

4*e^(-9*x^2 + 135)

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giac [A]  time = 0.14, size = 10, normalized size = 0.91 \begin {gather*} 4 \, e^{\left (-9 \, x^{2} + 135\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-72*x/exp(9*x^2-135),x, algorithm="giac")

[Out]

4*e^(-9*x^2 + 135)

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maple [A]  time = 0.03, size = 11, normalized size = 1.00

method	result	size
risch	\(4 \,{\mathrm e}^{-9 x^{2}+135}\)	\(11\)
gosper	\(4 \,{\mathrm e}^{-9 x^{2}+135}\)	\(13\)
derivativedivides	\(4 \,{\mathrm e}^{-9 x^{2}+135}\)	\(13\)
default	\(4 \,{\mathrm e}^{-9 x^{2}+135}\)	\(13\)
norman	\(4 \,{\mathrm e}^{-9 x^{2}+135}\)	\(13\)
meijerg	\(-4 \,{\mathrm e}^{-9 x^{2}+9 x^{2} {\mathrm e}^{135}} \left (1-{\mathrm e}^{-9 x^{2} {\mathrm e}^{135}}\right )\)	\(29\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-72*x/exp(9*x^2-135),x,method=_RETURNVERBOSE)

[Out]

4*exp(-9*x^2+135)

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maxima [A]  time = 0.47, size = 10, normalized size = 0.91 \begin {gather*} 4 \, e^{\left (-9 \, x^{2} + 135\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-72*x/exp(9*x^2-135),x, algorithm="maxima")

[Out]

4*e^(-9*x^2 + 135)

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mupad [B]  time = 0.06, size = 10, normalized size = 0.91 \begin {gather*} 4\,{\mathrm {e}}^{135}\,{\mathrm {e}}^{-9\,x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-72*x*exp(135 - 9*x^2),x)

[Out]

4*exp(135)*exp(-9*x^2)

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sympy [A]  time = 0.09, size = 8, normalized size = 0.73 \begin {gather*} 4 e^{135 - 9 x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-72*x/exp(9*x**2-135),x)

[Out]

4*exp(135 - 9*x**2)

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