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

Optimal. Leaf size=17 \[ e^{-3-e^5-6 x+2 x^2} \]

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Rubi [A]  time = 0.02, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {2236} \begin {gather*} e^{2 x^2-6 x-e^5-3} \end {gather*}

Antiderivative was successfully verified.

[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 2236

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 {gather*} \begin {aligned} \text {integral} &=e^{-3-e^5-6 x+2 x^2}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.03, size = 17, normalized size = 1.00 \begin {gather*} e^{-3-e^5-6 x+2 x^2} \end {gather*}

Antiderivative was successfully verified.

[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)

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fricas [A]  time = 0.75, size = 15, normalized size = 0.88 \begin {gather*} e^{\left (2 \, x^{2} - 6 \, x - e^{5} - 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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giac [A]  time = 0.21, size = 15, normalized size = 0.88 \begin {gather*} e^{\left (2 \, x^{2} - 6 \, x - e^{5} - 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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maple [A]  time = 0.05, size = 16, normalized size = 0.94

method	result	size
default	\({\mathrm e}^{-{\mathrm e}^{5}+2 x^{2}-6 x -3}\)	\(16\)
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	\({\mathrm e}^{-{\mathrm e}^{5}+2 x^{2}-2 x -3} {\mathrm e}^{-4 x}\)	\(23\)

Verification of antiderivative is not currently implemented for this CAS.

[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)

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maxima [A]  time = 0.41, size = 15, normalized size = 0.88 \begin {gather*} e^{\left (2 \, x^{2} - 6 \, x - e^{5} - 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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mupad [B]  time = 1.38, size = 18, normalized size = 1.06 \begin {gather*} {\mathrm {e}}^{-{\mathrm {e}}^5}\,{\mathrm {e}}^{-6\,x}\,{\mathrm {e}}^{-3}\,{\mathrm {e}}^{2\,x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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sympy [A]  time = 0.17, size = 19, normalized size = 1.12 \begin {gather*} e^{- 4 x} e^{2 x^{2} - 2 x - e^{5} - 3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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