3.60.45 \(\int \frac {24 e^{-\frac {8}{x^3 \log (3)}}}{x^4 \log (3)} \, dx\)

Optimal. Leaf size=11 \[ e^{-\frac {8}{x^3 \log (3)}} \]

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Rubi [A]  time = 0.03, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {12, 2209} \begin {gather*} e^{-\frac {8}{x^3 \log (3)}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[24/(E^(8/(x^3*Log[3]))*x^4*Log[3]),x]

[Out]

E^(-8/(x^3*Log[3]))

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 2209

Int[(F_)^((a_.) + (b_.)*((c_.) + (d_.)*(x_))^(n_))*((e_.) + (f_.)*(x_))^(m_.), x_Symbol] :> Simp[((e + f*x)^n*
F^(a + b*(c + d*x)^n))/(b*f*n*(c + d*x)^n*Log[F]), x] /; FreeQ[{F, a, b, c, d, e, f, n}, x] && EqQ[m, n - 1] &
& EqQ[d*e - c*f, 0]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {24 \int \frac {e^{-\frac {8}{x^3 \log (3)}}}{x^4} \, dx}{\log (3)}\\ &=e^{-\frac {8}{x^3 \log (3)}}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} e^{-\frac {8}{x^3 \log (3)}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[24/(E^(8/(x^3*Log[3]))*x^4*Log[3]),x]

[Out]

E^(-8/(x^3*Log[3]))

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fricas [A]  time = 0.72, size = 10, normalized size = 0.91 \begin {gather*} e^{\left (-\frac {8}{x^{3} \log \relax (3)}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(24*exp(-8/x^3/log(3))/x^4/log(3),x, algorithm="fricas")

[Out]

e^(-8/(x^3*log(3)))

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giac [A]  time = 0.22, size = 10, normalized size = 0.91 \begin {gather*} e^{\left (-\frac {8}{x^{3} \log \relax (3)}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(24*exp(-8/x^3/log(3))/x^4/log(3),x, algorithm="giac")

[Out]

e^(-8/(x^3*log(3)))

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maple [A]  time = 0.07, size = 11, normalized size = 1.00

method	result	size
gosper	\({\mathrm e}^{-\frac {8}{x^{3} \ln \relax (3)}}\)	\(11\)
derivativedivides	\({\mathrm e}^{-\frac {8}{x^{3} \ln \relax (3)}}\)	\(11\)
default	\({\mathrm e}^{-\frac {8}{x^{3} \ln \relax (3)}}\)	\(11\)
norman	\({\mathrm e}^{-\frac {8}{x^{3} \ln \relax (3)}}\)	\(11\)
risch	\({\mathrm e}^{-\frac {8}{x^{3} \ln \relax (3)}}\)	\(11\)
meijerg	\(-1+{\mathrm e}^{-\frac {8}{x^{3} \ln \relax (3)}}\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(24*exp(-8/x^3/ln(3))/x^4/ln(3),x,method=_RETURNVERBOSE)

[Out]

exp(-8/x^3/ln(3))

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maxima [A]  time = 0.44, size = 10, normalized size = 0.91 \begin {gather*} e^{\left (-\frac {8}{x^{3} \log \relax (3)}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(24*exp(-8/x^3/log(3))/x^4/log(3),x, algorithm="maxima")

[Out]

e^(-8/(x^3*log(3)))

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mupad [B]  time = 4.16, size = 10, normalized size = 0.91 \begin {gather*} {\mathrm {e}}^{-\frac {8}{x^3\,\ln \relax (3)}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((24*exp(-8/(x^3*log(3))))/(x^4*log(3)),x)

[Out]

exp(-8/(x^3*log(3)))

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sympy [A]  time = 0.12, size = 10, normalized size = 0.91 \begin {gather*} e^{- \frac {8}{x^{3} \log {\relax (3 )}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(24*exp(-8/x**3/ln(3))/x**4/ln(3),x)

[Out]

exp(-8/(x**3*log(3)))

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