3.66.6 \(\int 8 e^{8+2 x} \, dx\)

Optimal. Leaf size=11 \[ 5+4 e^{8+2 x} \]

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Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.82, number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 2194} \begin {gather*} 4 e^{2 x+8} \end {gather*}

Antiderivative was successfully verified.

[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 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} &=8 \int e^{8+2 x} \, dx\\ &=4 e^{8+2 x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 0.82 \begin {gather*} 4 e^{8+2 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[8*E^(8 + 2*x),x]

[Out]

4*E^(8 + 2*x)

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fricas [A]  time = 0.59, size = 8, normalized size = 0.73 \begin {gather*} 4 \, e^{\left (2 \, x + 8\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

4*e^(2*x + 8)

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giac [A]  time = 0.13, size = 8, normalized size = 0.73 \begin {gather*} 4 \, e^{\left (2 \, x + 8\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

4*e^(2*x + 8)

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maple [A]  time = 0.02, size = 9, normalized size = 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	\(4 \,{\mathrm e}^{2 x +8}\)	\(9\)
meijerg	\(-4 \,{\mathrm e}^{2 x -2 x \,{\mathrm e}^{8}} \left (1-{\mathrm e}^{2 x \,{\mathrm e}^{8}}\right )\)	\(23\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

4*exp(4+x)^2

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maxima [A]  time = 0.36, size = 8, normalized size = 0.73 \begin {gather*} 4 \, e^{\left (2 \, x + 8\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

4*e^(2*x + 8)

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mupad [B]  time = 0.03, size = 8, normalized size = 0.73 \begin {gather*} 4\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^8 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(8*exp(2*x + 8),x)

[Out]

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

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sympy [A]  time = 0.07, size = 7, normalized size = 0.64 \begin {gather*} 4 e^{2 x + 8} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

4*exp(2*x + 8)

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