3.14.81 \(\int -12 e^{-10-x} \, dx\)

Optimal. Leaf size=14 \[ \frac {4 \left (-2+3 e^{-x}\right )}{e^{10}} \]

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Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.64, 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*} 12 e^{-x-10} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-12*E^(-10 - x),x]

[Out]

12*E^(-10 - 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 (12 \int e^{-10-x} \, dx\right )\\ &=12 e^{-10-x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 0.64 \begin {gather*} 12 e^{-10-x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-12*E^(-10 - x),x]

[Out]

12*E^(-10 - x)

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fricas [A]  time = 0.61, size = 8, normalized size = 0.57 \begin {gather*} 12 \, e^{\left (-x - 10\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-12/exp(1)^2/exp(4)^2/exp(x),x, algorithm="fricas")

[Out]

12*e^(-x - 10)

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giac [A]  time = 0.73, size = 8, normalized size = 0.57 \begin {gather*} 12 \, e^{\left (-x - 10\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-12/exp(1)^2/exp(4)^2/exp(x),x, algorithm="giac")

[Out]

12*e^(-x - 10)

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maple [A]  time = 0.02, size = 9, normalized size = 0.64

method	result	size
risch	\(12 \,{\mathrm e}^{-10-x}\)	\(9\)
meijerg	\(-12 \,{\mathrm e}^{-10} \left (1-{\mathrm e}^{-x}\right )\)	\(13\)
gosper	\(12 \,{\mathrm e}^{-2} {\mathrm e}^{-8} {\mathrm e}^{-x}\)	\(15\)
derivativedivides	\(12 \,{\mathrm e}^{-2} {\mathrm e}^{-8} {\mathrm e}^{-x}\)	\(15\)
default	\(12 \,{\mathrm e}^{-2} {\mathrm e}^{-8} {\mathrm e}^{-x}\)	\(15\)
norman	\(12 \,{\mathrm e}^{-2} {\mathrm e}^{-8} {\mathrm e}^{-x}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-12/exp(1)^2/exp(4)^2/exp(x),x,method=_RETURNVERBOSE)

[Out]

12*exp(-10-x)

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maxima [A]  time = 0.46, size = 8, normalized size = 0.57 \begin {gather*} 12 \, e^{\left (-x - 10\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-12/exp(1)^2/exp(4)^2/exp(x),x, algorithm="maxima")

[Out]

12*e^(-x - 10)

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mupad [B]  time = 0.03, size = 8, normalized size = 0.57 \begin {gather*} 12\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{-10} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-12*exp(-x)*exp(-10),x)

[Out]

12*exp(-x)*exp(-10)

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sympy [A]  time = 0.08, size = 7, normalized size = 0.50 \begin {gather*} \frac {12 e^{- x}}{e^{10}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-12/exp(1)**2/exp(4)**2/exp(x),x)

[Out]

12*exp(-10)*exp(-x)

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