3.11.95 \(\int 60 e^{-84+60 x} \, dx\) [1095]

Optimal. Leaf size=13 \[ e^{4 (-1+5 (-4+3 x))} \]

[Out]

exp(60*x-84)

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Rubi [A]
time = 0.00, antiderivative size = 7, normalized size of antiderivative = 0.54, 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, 2225} \begin {gather*} e^{60 x-84} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[60*E^(-84 + 60*x),x]

[Out]

E^(-84 + 60*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 2225

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} &=60 \int e^{-84+60 x} \, dx\\ &=e^{-84+60 x}\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.01, size = 7, normalized size = 0.54 \begin {gather*} e^{-84+60 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[60*E^(-84 + 60*x),x]

[Out]

E^(-84 + 60*x)

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Maple [A]
time = 0.04, size = 7, normalized size = 0.54

method	result	size
gosper	\({\mathrm e}^{60 x -84}\)	\(7\)
derivativedivides	\({\mathrm e}^{60 x -84}\)	\(7\)
default	\({\mathrm e}^{60 x -84}\)	\(7\)
norman	\({\mathrm e}^{60 x -84}\)	\(7\)
risch	\({\mathrm e}^{60 x -84}\)	\(7\)
meijerg	\(-{\mathrm e}^{-84} \left (1-{\mathrm e}^{60 x}\right )\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(60*exp(60*x-84),x,method=_RETURNVERBOSE)

[Out]

exp(60*x-84)

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Maxima [A]
time = 0.26, size = 6, normalized size = 0.46 \begin {gather*} e^{\left (60 \, x - 84\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(60*exp(60*x-84),x, algorithm="maxima")

[Out]

e^(60*x - 84)

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Fricas [A]
time = 0.35, size = 6, normalized size = 0.46 \begin {gather*} e^{\left (60 \, x - 84\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(60*exp(60*x-84),x, algorithm="fricas")

[Out]

e^(60*x - 84)

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Sympy [A]
time = 0.02, size = 5, normalized size = 0.38 \begin {gather*} e^{60 x - 84} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(60*exp(60*x-84),x)

[Out]

exp(60*x - 84)

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Giac [A]
time = 0.38, size = 6, normalized size = 0.46 \begin {gather*} e^{\left (60 \, x - 84\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(60*exp(60*x-84),x, algorithm="giac")

[Out]

e^(60*x - 84)

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Mupad [B]
time = 0.70, size = 7, normalized size = 0.54 \begin {gather*} {\mathrm {e}}^{60\,x}\,{\mathrm {e}}^{-84} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(60*exp(60*x - 84),x)

[Out]

exp(60*x)*exp(-84)

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