3.83.72 \(\int -2 e^{2 x} \, dx\)

Optimal. Leaf size=9 \[ -10-e^{2 x} \]

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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*} -e^{2 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-2*E^(2*x),x]

[Out]

-E^(2*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 (2 \int e^{2 x} \, dx\right )\\ &=-e^{2 x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 7, normalized size = 0.78 \begin {gather*} -e^{2 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-2*E^(2*x),x]

[Out]

-E^(2*x)

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fricas [A]  time = 0.95, size = 6, normalized size = 0.67 \begin {gather*} -e^{\left (2 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*exp(x)^2,x, algorithm="fricas")

[Out]

-e^(2*x)

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giac [A]  time = 0.19, size = 6, normalized size = 0.67 \begin {gather*} -e^{\left (2 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*exp(x)^2,x, algorithm="giac")

[Out]

-e^(2*x)

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maple [A]  time = 0.02, size = 7, normalized size = 0.78

method	result	size
gosper	\(-{\mathrm e}^{2 x}\)	\(7\)
derivativedivides	\(-{\mathrm e}^{2 x}\)	\(7\)
default	\(-{\mathrm e}^{2 x}\)	\(7\)
norman	\(-{\mathrm e}^{2 x}\)	\(7\)
risch	\(-{\mathrm e}^{2 x}\)	\(7\)
meijerg	\(1-{\mathrm e}^{2 x}\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-2*exp(x)^2,x,method=_RETURNVERBOSE)

[Out]

-exp(x)^2

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maxima [A]  time = 0.42, size = 6, normalized size = 0.67 \begin {gather*} -e^{\left (2 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*exp(x)^2,x, algorithm="maxima")

[Out]

-e^(2*x)

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mupad [B]  time = 0.02, size = 6, normalized size = 0.67 \begin {gather*} -{\mathrm {e}}^{2\,x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-2*exp(2*x),x)

[Out]

-exp(2*x)

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sympy [A]  time = 0.04, size = 5, normalized size = 0.56 \begin {gather*} - e^{2 x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2*exp(x)**2,x)

[Out]

-exp(2*x)

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