3.93.73 \(\int -2 e^{4+\sqrt {e}-e^3-x} \, dx\)

Optimal. Leaf size=19 \[ 2 e^{4+\sqrt {e}-e^3-x} \]

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Rubi [A]  time = 0.01, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {12, 2194} \begin {gather*} 2 e^{-x-e^3+\sqrt {e}+4} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-2*E^(4 + Sqrt[E] - E^3 - x),x]

[Out]

2*E^(4 + Sqrt[E] - E^3 - x)

Rule 12

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

Rule 2194

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\left (2 \int e^{4+\sqrt {e}-e^3-x} \, dx\right )\\ &=2 e^{4+\sqrt {e}-e^3-x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 19, normalized size = 1.00 \begin {gather*} 2 e^{4+\sqrt {e}-e^3-x} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

2*E^(4 + Sqrt[E] - E^3 - x)

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fricas [A]  time = 0.63, size = 14, normalized size = 0.74 \begin {gather*} 2 \, e^{\left (-x - e^{3} + e^{\frac {1}{2}} + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2/exp(exp(3)-exp(1/2)+x-4),x, algorithm="fricas")

[Out]

2*e^(-x - e^3 + e^(1/2) + 4)

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giac [A]  time = 0.19, size = 14, normalized size = 0.74 \begin {gather*} 2 \, e^{\left (-x - e^{3} + e^{\frac {1}{2}} + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2/exp(exp(3)-exp(1/2)+x-4),x, algorithm="giac")

[Out]

2*e^(-x - e^3 + e^(1/2) + 4)

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maple [A]  time = 0.02, size = 15, normalized size = 0.79

method	result	size
gosper	\(2 \,{\mathrm e}^{-{\mathrm e}^{3}+{\mathrm e}^{\frac {1}{2}}-x +4}\)	\(15\)
derivativedivides	\(2 \,{\mathrm e}^{-{\mathrm e}^{3}+{\mathrm e}^{\frac {1}{2}}-x +4}\)	\(15\)
default	\(2 \,{\mathrm e}^{-{\mathrm e}^{3}+{\mathrm e}^{\frac {1}{2}}-x +4}\)	\(15\)
norman	\(2 \,{\mathrm e}^{-{\mathrm e}^{3}+{\mathrm e}^{\frac {1}{2}}-x +4}\)	\(15\)
risch	\(2 \,{\mathrm e}^{-{\mathrm e}^{3}+{\mathrm e}^{\frac {1}{2}}-x +4}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-2/exp(exp(3)-exp(1/2)+x-4),x,method=_RETURNVERBOSE)

[Out]

2/exp(exp(3)-exp(1/2)+x-4)

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maxima [A]  time = 0.36, size = 14, normalized size = 0.74 \begin {gather*} 2 \, e^{\left (-x - e^{3} + e^{\frac {1}{2}} + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2/exp(exp(3)-exp(1/2)+x-4),x, algorithm="maxima")

[Out]

2*e^(-x - e^3 + e^(1/2) + 4)

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mupad [B]  time = 0.04, size = 16, normalized size = 0.84 \begin {gather*} 2\,{\mathrm {e}}^{-{\mathrm {e}}^3}\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^4\,{\mathrm {e}}^{\sqrt {\mathrm {e}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-2*exp(exp(1/2) - x - exp(3) + 4),x)

[Out]

2*exp(-exp(3))*exp(-x)*exp(4)*exp(exp(1/2))

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sympy [A]  time = 0.08, size = 14, normalized size = 0.74 \begin {gather*} 2 e^{- x - e^{3} + e^{\frac {1}{2}} + 4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2/exp(exp(3)-exp(1/2)+x-4),x)

[Out]

2*exp(-x - exp(3) + exp(1/2) + 4)

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