3.27.16 \(\int -8 e^{4-8 x} \, dx\)

Optimal. Leaf size=14 \[ e^{\frac {4 \left (x-2 x^2\right )}{x}} \]

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Rubi [A]  time = 0.00, antiderivative size = 7, normalized size of antiderivative = 0.50, number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 2194} \begin {gather*} e^{4-8 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-8*E^(4 - 8*x),x]

[Out]

E^(4 - 8*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 (8 \int e^{4-8 x} \, dx\right )\\ &=e^{4-8 x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 7, normalized size = 0.50 \begin {gather*} e^{4-8 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-8*E^(4 - 8*x),x]

[Out]

E^(4 - 8*x)

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fricas [A]  time = 0.58, size = 6, normalized size = 0.43 \begin {gather*} e^{\left (-8 \, x + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8*exp(-8*x+4),x, algorithm="fricas")

[Out]

e^(-8*x + 4)

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giac [A]  time = 0.30, size = 6, normalized size = 0.43 \begin {gather*} e^{\left (-8 \, x + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8*exp(-8*x+4),x, algorithm="giac")

[Out]

e^(-8*x + 4)

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maple [A]  time = 0.01, size = 7, normalized size = 0.50

method	result	size
gosper	\({\mathrm e}^{-8 x +4}\)	\(7\)
derivativedivides	\({\mathrm e}^{-8 x +4}\)	\(7\)
default	\({\mathrm e}^{-8 x +4}\)	\(7\)
norman	\({\mathrm e}^{-8 x +4}\)	\(7\)
risch	\({\mathrm e}^{-8 x +4}\)	\(7\)
meijerg	\(-{\mathrm e}^{4} \left (1-{\mathrm e}^{-8 x}\right )\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-8*exp(-8*x+4),x,method=_RETURNVERBOSE)

[Out]

exp(-8*x+4)

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maxima [A]  time = 0.42, size = 6, normalized size = 0.43 \begin {gather*} e^{\left (-8 \, x + 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8*exp(-8*x+4),x, algorithm="maxima")

[Out]

e^(-8*x + 4)

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mupad [B]  time = 0.03, size = 7, normalized size = 0.50 \begin {gather*} {\mathrm {e}}^{-8\,x}\,{\mathrm {e}}^4 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-8*exp(4 - 8*x),x)

[Out]

exp(-8*x)*exp(4)

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sympy [A]  time = 0.07, size = 5, normalized size = 0.36 \begin {gather*} e^{4 - 8 x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8*exp(-8*x+4),x)

[Out]

exp(4 - 8*x)

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