3.35.9 \(\int -30 e^{-x} \, dx\)

Optimal. Leaf size=9 \[ -5+30 e^{-x} \]

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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 = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {12, 2194} \begin {gather*} 30 e^{-x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-30/E^x,x]

[Out]

30/E^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 (30 \int e^{-x} \, dx\right )\\ &=30 e^{-x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 7, normalized size = 0.78 \begin {gather*} 30 e^{-x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-30/E^x,x]

[Out]

30/E^x

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fricas [A]  time = 0.86, size = 6, normalized size = 0.67 \begin {gather*} 30 \, e^{\left (-x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-30/exp(x),x, algorithm="fricas")

[Out]

30*e^(-x)

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giac [A]  time = 0.13, size = 6, normalized size = 0.67 \begin {gather*} 30 \, e^{\left (-x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-30/exp(x),x, algorithm="giac")

[Out]

30*e^(-x)

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

method	result	size
gosper	\(30 \,{\mathrm e}^{-x}\)	\(7\)
derivativedivides	\(30 \,{\mathrm e}^{-x}\)	\(7\)
default	\(30 \,{\mathrm e}^{-x}\)	\(7\)
norman	\(30 \,{\mathrm e}^{-x}\)	\(7\)
risch	\(30 \,{\mathrm e}^{-x}\)	\(7\)
meijerg	\(-30+30 \,{\mathrm e}^{-x}\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-30/exp(x),x,method=_RETURNVERBOSE)

[Out]

30/exp(x)

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maxima [A]  time = 0.63, size = 6, normalized size = 0.67 \begin {gather*} 30 \, e^{\left (-x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-30/exp(x),x, algorithm="maxima")

[Out]

30*e^(-x)

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mupad [B]  time = 0.01, size = 6, normalized size = 0.67 \begin {gather*} 30\,{\mathrm {e}}^{-x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-30*exp(-x),x)

[Out]

30*exp(-x)

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sympy [A]  time = 0.04, size = 3, normalized size = 0.33 \begin {gather*} 30 e^{- x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-30/exp(x),x)

[Out]

30*exp(-x)

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