\(\int -2 e^{2 x} \, dx\) [8272]

Optimal result

Integrand size = 7, antiderivative size = 9 \[ \int -2 e^{2 x} \, dx=-10-e^{2 x} \]

[Out]

-exp(x)^2-10

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {12, 2225} \[ \int -2 e^{2 x} \, dx=-e^{2 x} \]

[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 2225

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{align*} \text {integral}& = -\left (2 \int e^{2 x} \, dx\right ) \\ & = -e^{2 x} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int -2 e^{2 x} \, dx=-e^{2 x} \]

[In]

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

[Out]

-E^(2*x)

Maple [A] (verified)

Time = 0.06 (sec) , antiderivative size = 7, normalized size of antiderivative = 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	\(-{\mathrm e}^{2 x}\)	\(7\)
parallelrisch	\(-{\mathrm e}^{2 x}\)	\(7\)
meijerg	\(1-{\mathrm e}^{2 x}\)	\(9\)

[In]

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

[Out]

-exp(x)^2

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int -2 e^{2 x} \, dx=-e^{\left (2 \, x\right )} \]

[In]

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

[Out]

-e^(2*x)

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.56 \[ \int -2 e^{2 x} \, dx=- e^{2 x} \]

[In]

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

[Out]

-exp(2*x)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int -2 e^{2 x} \, dx=-e^{\left (2 \, x\right )} \]

[In]

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

[Out]

-e^(2*x)

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int -2 e^{2 x} \, dx=-e^{\left (2 \, x\right )} \]

[In]

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

[Out]

-e^(2*x)

Mupad [B] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int -2 e^{2 x} \, dx=-{\mathrm {e}}^{2\,x} \]

[In]

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

[Out]

-exp(2*x)