3.33.6 \(\int 3 e^{-18+3 x} \, dx\)

Optimal. Leaf size=9 \[ e^{-3 (6-x)} \]

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Rubi [A]  time = 0.00, antiderivative size = 7, normalized size of antiderivative = 0.78, 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^{3 x-18} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[3*E^(-18 + 3*x),x]

[Out]

E^(-18 + 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} &=3 \int e^{-18+3 x} \, dx\\ &=e^{-18+3 x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 7, normalized size = 0.78 \begin {gather*} e^{-18+3 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[3*E^(-18 + 3*x),x]

[Out]

E^(-18 + 3*x)

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fricas [A]  time = 0.50, size = 6, normalized size = 0.67 \begin {gather*} e^{\left (3 \, x - 18\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*exp(3*x-18),x, algorithm="fricas")

[Out]

e^(3*x - 18)

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giac [A]  time = 0.17, size = 6, normalized size = 0.67 \begin {gather*} e^{\left (3 \, x - 18\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*exp(3*x-18),x, algorithm="giac")

[Out]

e^(3*x - 18)

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maple [A]  time = 0.01, size = 7, normalized size = 0.78

method	result	size
gosper	\({\mathrm e}^{3 x -18}\)	\(7\)
derivativedivides	\({\mathrm e}^{3 x -18}\)	\(7\)
default	\({\mathrm e}^{3 x -18}\)	\(7\)
norman	\({\mathrm e}^{3 x -18}\)	\(7\)
risch	\({\mathrm e}^{3 x -18}\)	\(7\)
meijerg	\(-{\mathrm e}^{-18} \left (1-{\mathrm e}^{3 x}\right )\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3*exp(3*x-18),x,method=_RETURNVERBOSE)

[Out]

exp(3*x-18)

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maxima [A]  time = 0.75, size = 6, normalized size = 0.67 \begin {gather*} e^{\left (3 \, x - 18\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*exp(3*x-18),x, algorithm="maxima")

[Out]

e^(3*x - 18)

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mupad [B]  time = 1.84, size = 7, normalized size = 0.78 \begin {gather*} {\mathrm {e}}^{3\,x}\,{\mathrm {e}}^{-18} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3*exp(3*x - 18),x)

[Out]

exp(3*x)*exp(-18)

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sympy [A]  time = 0.08, size = 5, normalized size = 0.56 \begin {gather*} e^{3 x - 18} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*exp(3*x-18),x)

[Out]

exp(3*x - 18)

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