\(\int -72 e^{135-9 x^2} x \, dx\) [3501]

Optimal result

Integrand size = 12, antiderivative size = 11 \[ \int -72 e^{135-9 x^2} x \, dx=4 e^{-9 \left (-15+x^2\right )} \]

[Out]

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

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {12, 2240} \[ \int -72 e^{135-9 x^2} x \, dx=4 e^{135-9 x^2} \]

[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 2240

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{align*} \text {integral}& = -\left (72 \int e^{135-9 x^2} x \, dx\right ) \\ & = 4 e^{135-9 x^2} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.02 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int -72 e^{135-9 x^2} x \, dx=4 e^{135-9 x^2} \]

[In]

Integrate[-72*E^(135 - 9*x^2)*x,x]

[Out]

4*E^(135 - 9*x^2)

Maple [A] (verified)

Time = 0.59 (sec) , antiderivative size = 11, normalized size of antiderivative = 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	\(4 \,{\mathrm e}^{-9 x^{2}+135}\)	\(13\)
parallelrisch	\(4 \,{\mathrm e}^{-9 x^{2}+135}\)	\(13\)
meijerg	\(-4 \,{\mathrm e}^{-9 x^{2}+9 x^{2} {\mathrm e}^{135}} \left (1-{\mathrm e}^{-9 x^{2} {\mathrm e}^{135}}\right )\)	\(29\)

[In]

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

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.91 \[ \int -72 e^{135-9 x^2} x \, dx=4 \, e^{\left (-9 \, x^{2} + 135\right )} \]

[In]

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

[Out]

4*e^(-9*x^2 + 135)

Sympy [A] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int -72 e^{135-9 x^2} x \, dx=4 e^{135 - 9 x^{2}} \]

[In]

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

[Out]

4*exp(135 - 9*x**2)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.91 \[ \int -72 e^{135-9 x^2} x \, dx=4 \, e^{\left (-9 \, x^{2} + 135\right )} \]

[In]

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

[Out]

4*e^(-9*x^2 + 135)

Giac [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.91 \[ \int -72 e^{135-9 x^2} x \, dx=4 \, e^{\left (-9 \, x^{2} + 135\right )} \]

[In]

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

[Out]

4*e^(-9*x^2 + 135)

Mupad [B] (verification not implemented)

Time = 0.06 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.91 \[ \int -72 e^{135-9 x^2} x \, dx=4\,{\mathrm {e}}^{135}\,{\mathrm {e}}^{-9\,x^2} \]

[In]

int(-72*x*exp(135 - 9*x^2),x)

[Out]

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