3.31.20 \(\int -\frac {32\ 3^{-2/x} \log (3)}{x^2} \, dx\)

Optimal. Leaf size=15 \[ 3 \left (-2-16\ 3^{-1-\frac {2}{x}}\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 9, normalized size of antiderivative = 0.60, number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 2209} \begin {gather*} -16 3^{-2/x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-32*Log[3])/(3^(2/x)*x^2),x]

[Out]

-16/3^(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 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} &=-\left ((32 \log (3)) \int \frac {3^{-2/x}}{x^2} \, dx\right )\\ &=-16 3^{-2/x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} -\frac {32\ 9^{-1/x} \log (3)}{\log (9)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-32*Log[3])/(3^(2/x)*x^2),x]

[Out]

(-32*Log[3])/(9^x^(-1)*Log[9])

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fricas [A]  time = 0.63, size = 11, normalized size = 0.73 \begin {gather*} -\frac {16}{3^{\frac {2}{x}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-32*log(3)/x^2/exp(2*log(3)/x),x, algorithm="fricas")

[Out]

-16/3^(2/x)

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giac [A]  time = 0.21, size = 11, normalized size = 0.73 \begin {gather*} -\frac {16}{3^{\frac {2}{x}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-32*log(3)/x^2/exp(2*log(3)/x),x, algorithm="giac")

[Out]

-16/3^(2/x)

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maple [A]  time = 0.04, size = 10, normalized size = 0.67

method	result	size
risch	\(-16 \,9^{-\frac {1}{x}}\)	\(10\)
gosper	\(-16 \,{\mathrm e}^{-\frac {2 \ln \relax (3)}{x}}\)	\(13\)
derivativedivides	\(-16 \,{\mathrm e}^{-\frac {2 \ln \relax (3)}{x}}\)	\(13\)
default	\(-16 \,{\mathrm e}^{-\frac {2 \ln \relax (3)}{x}}\)	\(13\)
norman	\(-16 \,{\mathrm e}^{-\frac {2 \ln \relax (3)}{x}}\)	\(13\)
meijerg	\(16-16 \,{\mathrm e}^{-\frac {2 \ln \relax (3)}{x}}\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-32*ln(3)/x^2/exp(2*ln(3)/x),x,method=_RETURNVERBOSE)

[Out]

-16/(9^(1/x))

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maxima [A]  time = 0.39, size = 11, normalized size = 0.73 \begin {gather*} -\frac {16}{3^{\frac {2}{x}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-32*log(3)/x^2/exp(2*log(3)/x),x, algorithm="maxima")

[Out]

-16/3^(2/x)

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mupad [B]  time = 1.74, size = 11, normalized size = 0.73 \begin {gather*} -\frac {16}{3^{2/x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(32*exp(-(2*log(3))/x)*log(3))/x^2,x)

[Out]

-16/3^(2/x)

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sympy [A]  time = 0.11, size = 10, normalized size = 0.67 \begin {gather*} - 16 e^{- \frac {2 \log {\relax (3 )}}{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-32*ln(3)/x**2/exp(2*ln(3)/x),x)

[Out]

-16*exp(-2*log(3)/x)

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