\(\int e^{-3-e^5-6 x+2 x^2} (-6+4 x) \, dx\) [2330]

Optimal result

Integrand size = 23, antiderivative size = 17 \[ \int e^{-3-e^5-6 x+2 x^2} (-6+4 x) \, dx=e^{-3-e^5-6 x+2 x^2} \]

[Out]

exp(-exp(5)+2*x^2-2*x-3)/exp(4*x)

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {2268} \[ \int e^{-3-e^5-6 x+2 x^2} (-6+4 x) \, dx=e^{2 x^2-6 x-e^5-3} \]

[In]

Int[E^(-3 - E^5 - 6*x + 2*x^2)*(-6 + 4*x),x]

[Out]

E^(-3 - E^5 - 6*x + 2*x^2)

Rule 2268

Int[(F_)^((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)*((d_.) + (e_.)*(x_)), x_Symbol] :> Simp[e*(F^(a + b*x + c*x^2)/(2
*c*Log[F])), x] /; FreeQ[{F, a, b, c, d, e}, x] && EqQ[b*e - 2*c*d, 0]

Rubi steps \begin{align*} \text {integral}& = e^{-3-e^5-6 x+2 x^2} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.08 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00 \[ \int e^{-3-e^5-6 x+2 x^2} (-6+4 x) \, dx=e^{-3-e^5-6 x+2 x^2} \]

[In]

Integrate[E^(-3 - E^5 - 6*x + 2*x^2)*(-6 + 4*x),x]

[Out]

E^(-3 - E^5 - 6*x + 2*x^2)

Maple [A] (verified)

Time = 0.08 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.94

method	result	size
risch	\({\mathrm e}^{-{\mathrm e}^{5}+2 x^{2}-6 x -3}\)	\(16\)
gosper	\({\mathrm e}^{-{\mathrm e}^{5}+2 x^{2}-2 x -3} {\mathrm e}^{-4 x}\)	\(23\)
norman	\({\mathrm e}^{-{\mathrm e}^{5}+2 x^{2}-2 x -3} {\mathrm e}^{-4 x}\)	\(23\)
parallelrisch	\({\mathrm e}^{-{\mathrm e}^{5}+2 x^{2}-2 x -3} {\mathrm e}^{-4 x}\)	\(23\)
default	\(\frac {3 i {\mathrm e}^{-{\mathrm e}^{5}} {\mathrm e}^{-3} \sqrt {\pi }\, {\mathrm e}^{-\frac {9}{2}} \sqrt {2}\, \operatorname {erf}\left (i \sqrt {2}\, x -\frac {3 i \sqrt {2}}{2}\right )}{2}+4 \,{\mathrm e}^{-{\mathrm e}^{5}} {\mathrm e}^{-3} \left (\frac {{\mathrm e}^{2 x^{2}-6 x}}{4}-\frac {3 i \sqrt {\pi }\, {\mathrm e}^{-\frac {9}{2}} \sqrt {2}\, \operatorname {erf}\left (i \sqrt {2}\, x -\frac {3 i \sqrt {2}}{2}\right )}{8}\right )\)	\(83\)

[In]

int((4*x-6)*exp(-exp(5)+2*x^2-2*x-3)/exp(4*x),x,method=_RETURNVERBOSE)

[Out]

exp(-exp(5)+2*x^2-6*x-3)

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.88 \[ \int e^{-3-e^5-6 x+2 x^2} (-6+4 x) \, dx=e^{\left (2 \, x^{2} - 6 \, x - e^{5} - 3\right )} \]

[In]

integrate((4*x-6)*exp(-exp(5)+2*x^2-2*x-3)/exp(4*x),x, algorithm="fricas")

[Out]

e^(2*x^2 - 6*x - e^5 - 3)

Sympy [A] (verification not implemented)

Time = 0.09 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.12 \[ \int e^{-3-e^5-6 x+2 x^2} (-6+4 x) \, dx=e^{- 4 x} e^{2 x^{2} - 2 x - e^{5} - 3} \]

[In]

integrate((4*x-6)*exp(-exp(5)+2*x**2-2*x-3)/exp(4*x),x)

[Out]

exp(-4*x)*exp(2*x**2 - 2*x - exp(5) - 3)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.88 \[ \int e^{-3-e^5-6 x+2 x^2} (-6+4 x) \, dx=e^{\left (2 \, x^{2} - 6 \, x - e^{5} - 3\right )} \]

[In]

integrate((4*x-6)*exp(-exp(5)+2*x^2-2*x-3)/exp(4*x),x, algorithm="maxima")

[Out]

e^(2*x^2 - 6*x - e^5 - 3)

Giac [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.88 \[ \int e^{-3-e^5-6 x+2 x^2} (-6+4 x) \, dx=e^{\left (2 \, x^{2} - 6 \, x - e^{5} - 3\right )} \]

[In]

integrate((4*x-6)*exp(-exp(5)+2*x^2-2*x-3)/exp(4*x),x, algorithm="giac")

[Out]

e^(2*x^2 - 6*x - e^5 - 3)

Mupad [B] (verification not implemented)

Time = 9.42 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.06 \[ \int e^{-3-e^5-6 x+2 x^2} (-6+4 x) \, dx={\mathrm {e}}^{-{\mathrm {e}}^5}\,{\mathrm {e}}^{-6\,x}\,{\mathrm {e}}^{-3}\,{\mathrm {e}}^{2\,x^2} \]

[In]

int(exp(-4*x)*exp(2*x^2 - exp(5) - 2*x - 3)*(4*x - 6),x)

[Out]

exp(-exp(5))*exp(-6*x)*exp(-3)*exp(2*x^2)