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

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

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Rubi [A]  time = 0.00, antiderivative size = 5, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {2194} \begin {gather*} e^{-x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-E^(-x),x]

[Out]

E^(-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} &=e^{-x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 5, normalized size = 1.00 \begin {gather*} e^{-x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-E^(-x),x]

[Out]

E^(-x)

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fricas [A]  time = 1.11, size = 11, normalized size = 2.20 \begin {gather*} 3 \, e^{\left (-x - \log \relax (3)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/exp(log(3)+x),x, algorithm="fricas")

[Out]

3*e^(-x - log(3))

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giac [A]  time = 0.29, size = 11, normalized size = 2.20 \begin {gather*} 3 \, e^{\left (-x - \log \relax (3)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/exp(log(3)+x),x, algorithm="giac")

[Out]

3*e^(-x - log(3))

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maple [A]  time = 0.03, size = 5, normalized size = 1.00

method	result	size
risch	\({\mathrm e}^{-x}\)	\(5\)
gosper	\({\mathrm e}^{-x}\)	\(10\)
derivativedivides	\({\mathrm e}^{-x}\)	\(10\)
default	\({\mathrm e}^{-x}\)	\(10\)
norman	\({\mathrm e}^{-x}\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-3/exp(ln(3)+x),x,method=_RETURNVERBOSE)

[Out]

exp(-x)

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maxima [A]  time = 0.38, size = 4, normalized size = 0.80 \begin {gather*} e^{\left (-x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/exp(log(3)+x),x, algorithm="maxima")

[Out]

e^(-x)

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mupad [B]  time = 0.03, size = 4, normalized size = 0.80 \begin {gather*} {\mathrm {e}}^{-x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-3*exp(- x - log(3)),x)

[Out]

exp(-x)

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sympy [A]  time = 0.06, size = 3, normalized size = 0.60 \begin {gather*} e^{- x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3/exp(ln(3)+x),x)

[Out]

exp(-x)

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