3.22.72 \(\int \frac {448}{69} e^{\frac {1}{3} (-3 e^4+14 x)} \, dx\)

Optimal. Leaf size=21 \[ 2 \left (-3+\frac {16}{23} e^{-e^4+\frac {14 x}{3}}\right ) \]

________________________________________________________________________________________

Rubi [A]  time = 0.01, antiderivative size = 19, normalized size of antiderivative = 0.90, number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {12, 2194} \begin {gather*} \frac {32}{23} e^{\frac {1}{3} \left (14 x-3 e^4\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(448*E^((-3*E^4 + 14*x)/3))/69,x]

[Out]

(32*E^((-3*E^4 + 14*x)/3))/23

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} &=\frac {448}{69} \int e^{\frac {1}{3} \left (-3 e^4+14 x\right )} \, dx\\ &=\frac {32}{23} e^{\frac {1}{3} \left (-3 e^4+14 x\right )}\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 17, normalized size = 0.81 \begin {gather*} \frac {32}{23} e^{-e^4+\frac {14 x}{3}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(448*E^((-3*E^4 + 14*x)/3))/69,x]

[Out]

(32*E^(-E^4 + (14*x)/3))/23

________________________________________________________________________________________

fricas [A]  time = 0.46, size = 11, normalized size = 0.52 \begin {gather*} \frac {32}{23} \, e^{\left (\frac {14}{3} \, x - e^{4}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(448/69*exp(-exp(4)+14/3*x),x, algorithm="fricas")

[Out]

32/23*e^(14/3*x - e^4)

________________________________________________________________________________________

giac [A]  time = 0.22, size = 11, normalized size = 0.52 \begin {gather*} \frac {32}{23} \, e^{\left (\frac {14}{3} \, x - e^{4}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(448/69*exp(-exp(4)+14/3*x),x, algorithm="giac")

[Out]

32/23*e^(14/3*x - e^4)

________________________________________________________________________________________

maple [A]  time = 0.02, size = 12, normalized size = 0.57

method	result	size
gosper	\(\frac {32 \,{\mathrm e}^{-{\mathrm e}^{4}+\frac {14 x}{3}}}{23}\)	\(12\)
derivativedivides	\(\frac {32 \,{\mathrm e}^{-{\mathrm e}^{4}+\frac {14 x}{3}}}{23}\)	\(12\)
default	\(\frac {32 \,{\mathrm e}^{-{\mathrm e}^{4}+\frac {14 x}{3}}}{23}\)	\(12\)
norman	\(\frac {32 \,{\mathrm e}^{-{\mathrm e}^{4}+\frac {14 x}{3}}}{23}\)	\(12\)
risch	\(\frac {32 \,{\mathrm e}^{-{\mathrm e}^{4}+\frac {14 x}{3}}}{23}\)	\(12\)
meijerg	\(-\frac {32 \,{\mathrm e}^{-{\mathrm e}^{4}} \left (1-{\mathrm e}^{\frac {14 x}{3}}\right )}{23}\)	\(16\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(448/69*exp(-exp(4)+14/3*x),x,method=_RETURNVERBOSE)

[Out]

32/23*exp(-exp(4)+14/3*x)

________________________________________________________________________________________

maxima [A]  time = 0.69, size = 11, normalized size = 0.52 \begin {gather*} \frac {32}{23} \, e^{\left (\frac {14}{3} \, x - e^{4}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(448/69*exp(-exp(4)+14/3*x),x, algorithm="maxima")

[Out]

32/23*e^(14/3*x - e^4)

________________________________________________________________________________________

mupad [B]  time = 1.19, size = 11, normalized size = 0.52 \begin {gather*} \frac {32\,{\mathrm {e}}^{-{\mathrm {e}}^4}\,{\mathrm {e}}^{\frac {14\,x}{3}}}{23} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((448*exp((14*x)/3 - exp(4)))/69,x)

[Out]

(32*exp(-exp(4))*exp((14*x)/3))/23

________________________________________________________________________________________

sympy [A]  time = 0.08, size = 12, normalized size = 0.57 \begin {gather*} \frac {32 e^{\frac {14 x}{3} - e^{4}}}{23} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(448/69*exp(-exp(4)+14/3*x),x)

[Out]

32*exp(14*x/3 - exp(4))/23

________________________________________________________________________________________