3.78.56 \(\int -e^x \, dx\)

Optimal. Leaf size=15 \[ -e^x+\log ^2(2+e)+\log (\log (3)) \]

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Rubi [A]  time = 0.00, antiderivative size = 5, normalized size of antiderivative = 0.33, number of steps used = 1, number of rules used = 1, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, 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 = 0.33 \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 = 0.57, size = 4, normalized size = 0.27 \begin {gather*} -e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-e^x

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giac [A]  time = 0.20, size = 4, normalized size = 0.27 \begin {gather*} -e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-e^x

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maple [A]  time = 0.03, size = 5, normalized size = 0.33

method	result	size
gosper	\(-{\mathrm e}^{x}\)	\(5\)
derivativedivides	\(-{\mathrm e}^{x}\)	\(5\)
default	\(-{\mathrm e}^{x}\)	\(5\)
norman	\(-{\mathrm e}^{x}\)	\(5\)
risch	\(-{\mathrm e}^{x}\)	\(5\)
meijerg	\(1-{\mathrm e}^{x}\)	\(7\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-exp(x)

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maxima [A]  time = 0.35, size = 4, normalized size = 0.27 \begin {gather*} -e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-e^x

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mupad [B]  time = 0.01, size = 4, normalized size = 0.27 \begin {gather*} -{\mathrm {e}}^x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(x),x)

[Out]

-exp(x)

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sympy [A]  time = 0.04, size = 3, normalized size = 0.20 \begin {gather*} - e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(x),x)

[Out]

-exp(x)

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