3.20.39 \(\int -2 e^{\frac {2}{25} (695-e^4-25 x)} \, dx\)

Optimal. Leaf size=16 \[ e^{\frac {278}{5}-\frac {2 e^4}{25}-2 x} \]

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Rubi [A]  time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {12, 2194} \begin {gather*} e^{\frac {2}{25} \left (-25 x-e^4+695\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-2*E^((2*(695 - E^4 - 25*x))/25),x]

[Out]

E^((2*(695 - E^4 - 25*x))/25)

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^{\frac {2}{25} \left (695-e^4-25 x\right )} \, dx\right )\\ &=e^{\frac {2}{25} \left (695-e^4-25 x\right )}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 15, normalized size = 0.94 \begin {gather*} e^{-\frac {2}{25} \left (-695+e^4\right )-2 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-2*E^((2*(695 - E^4 - 25*x))/25),x]

[Out]

E^((-2*(-695 + E^4))/25 - 2*x)

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fricas [A]  time = 0.82, size = 10, normalized size = 0.62 \begin {gather*} e^{\left (-2 \, x - \frac {2}{25} \, e^{4} + \frac {278}{5}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*exp(-1/25*exp(4)-x+139/5)^2,x, algorithm="fricas")

[Out]

e^(-2*x - 2/25*e^4 + 278/5)

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giac [A]  time = 0.25, size = 10, normalized size = 0.62 \begin {gather*} e^{\left (-2 \, x - \frac {2}{25} \, e^{4} + \frac {278}{5}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*exp(-1/25*exp(4)-x+139/5)^2,x, algorithm="giac")

[Out]

e^(-2*x - 2/25*e^4 + 278/5)

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maple [A]  time = 0.02, size = 11, normalized size = 0.69

method	result	size
risch	\({\mathrm e}^{-\frac {2 \,{\mathrm e}^{4}}{25}-2 x +\frac {278}{5}}\)	\(11\)
gosper	\({\mathrm e}^{-\frac {2 \,{\mathrm e}^{4}}{25}-2 x +\frac {278}{5}}\)	\(13\)
derivativedivides	\({\mathrm e}^{-\frac {2 \,{\mathrm e}^{4}}{25}-2 x +\frac {278}{5}}\)	\(13\)
default	\({\mathrm e}^{-\frac {2 \,{\mathrm e}^{4}}{25}-2 x +\frac {278}{5}}\)	\(13\)
norman	\({\mathrm e}^{-\frac {2 \,{\mathrm e}^{4}}{25}-2 x +\frac {278}{5}}\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-2*exp(-1/25*exp(4)-x+139/5)^2,x,method=_RETURNVERBOSE)

[Out]

exp(-2/25*exp(4)-2*x+278/5)

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maxima [A]  time = 0.79, size = 10, normalized size = 0.62 \begin {gather*} e^{\left (-2 \, x - \frac {2}{25} \, e^{4} + \frac {278}{5}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*exp(-1/25*exp(4)-x+139/5)^2,x, algorithm="maxima")

[Out]

e^(-2*x - 2/25*e^4 + 278/5)

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mupad [B]  time = 0.03, size = 12, normalized size = 0.75 \begin {gather*} {\mathrm {e}}^{-\frac {2\,{\mathrm {e}}^4}{25}}\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{278/5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-2*exp(278/5 - (2*exp(4))/25 - 2*x),x)

[Out]

exp(-(2*exp(4))/25)*exp(-2*x)*exp(278/5)

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sympy [A]  time = 0.08, size = 14, normalized size = 0.88 \begin {gather*} e^{- 2 x - \frac {2 e^{4}}{25} + \frac {278}{5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*exp(-1/25*exp(4)-x+139/5)**2,x)

[Out]

exp(-2*x - 2*exp(4)/25 + 278/5)

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