\(\int 8 e^{8+2 x} \, dx\) [6506]

Optimal result

Integrand size = 9, antiderivative size = 11 \[ \int 8 e^{8+2 x} \, dx=5+4 e^{8+2 x} \]

[Out]

4*exp(4+x)^2+5

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 2225} \[ \int 8 e^{8+2 x} \, dx=4 e^{2 x+8} \]

[In]

Int[8*E^(8 + 2*x),x]

[Out]

4*E^(8 + 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}& = 8 \int e^{8+2 x} \, dx \\ & = 4 e^{8+2 x} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.01 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82 \[ \int 8 e^{8+2 x} \, dx=4 e^{8+2 x} \]

[In]

Integrate[8*E^(8 + 2*x),x]

[Out]

4*E^(8 + 2*x)

Maple [A] (verified)

Time = 0.08 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82

method	result	size
gosper	\(4 \,{\mathrm e}^{2 x +8}\)	\(9\)
derivativedivides	\(4 \,{\mathrm e}^{2 x +8}\)	\(9\)
default	\(4 \,{\mathrm e}^{2 x +8}\)	\(9\)
norman	\(4 \,{\mathrm e}^{2 x +8}\)	\(9\)
risch	\(4 \,{\mathrm e}^{2 x +8}\)	\(9\)
parallelrisch	\(4 \,{\mathrm e}^{2 x +8}\)	\(9\)
meijerg	\(-4 \,{\mathrm e}^{2 x -2 x \,{\mathrm e}^{8}} \left (1-{\mathrm e}^{2 x \,{\mathrm e}^{8}}\right )\)	\(23\)

[In]

int(8*exp(4+x)^2,x,method=_RETURNVERBOSE)

[Out]

4*exp(4+x)^2

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int 8 e^{8+2 x} \, dx=4 \, e^{\left (2 \, x + 8\right )} \]

[In]

integrate(8*exp(4+x)^2,x, algorithm="fricas")

[Out]

4*e^(2*x + 8)

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64 \[ \int 8 e^{8+2 x} \, dx=4 e^{2 x + 8} \]

[In]

integrate(8*exp(4+x)**2,x)

[Out]

4*exp(2*x + 8)

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int 8 e^{8+2 x} \, dx=4 \, e^{\left (2 \, x + 8\right )} \]

[In]

integrate(8*exp(4+x)^2,x, algorithm="maxima")

[Out]

4*e^(2*x + 8)

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int 8 e^{8+2 x} \, dx=4 \, e^{\left (2 \, x + 8\right )} \]

[In]

integrate(8*exp(4+x)^2,x, algorithm="giac")

[Out]

4*e^(2*x + 8)

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int 8 e^{8+2 x} \, dx=4\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^8 \]

[In]

int(8*exp(2*x + 8),x)

[Out]

4*exp(2*x)*exp(8)