3.77.40 \(\int -\frac {3 e \log (i \pi +\log (6))}{x^2} \, dx\)

Optimal. Leaf size=15 \[ \frac {3 e \log (i \pi +\log (6))}{x} \]

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Rubi [A]  time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {12, 30} \begin {gather*} \frac {3 e \log (\log (6)+i \pi )}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-3*E*Log[I*Pi + Log[6]])/x^2,x]

[Out]

(3*E*Log[I*Pi + Log[6]])/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 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\left ((3 e \log (i \pi +\log (6))) \int \frac {1}{x^2} \, dx\right )\\ &=\frac {3 e \log (i \pi +\log (6))}{x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} \frac {3 e \log (i \pi +\log (6))}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-3*E*Log[I*Pi + Log[6]])/x^2,x]

[Out]

(3*E*Log[I*Pi + Log[6]])/x

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fricas [A]  time = 0.99, size = 14, normalized size = 0.93 \begin {gather*} \frac {3 \, e \log \left (i \, \pi + \log \relax (6)\right )}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3*exp(1)*log(log(6)+I*pi)/x^2,x, algorithm="fricas")

[Out]

3*e*log(I*pi + log(6))/x

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giac [A]  time = 0.16, size = 14, normalized size = 0.93 \begin {gather*} \frac {3 \, e \log \left (i \, \pi + \log \relax (6)\right )}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3*exp(1)*log(log(6)+I*pi)/x^2,x, algorithm="giac")

[Out]

3*e*log(I*pi + log(6))/x

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maple [A]  time = 0.05, size = 16, normalized size = 1.07

method	result	size
gosper	\(\frac {3 \,{\mathrm e} \ln \left (\ln \relax (6)+i \pi \right )}{x}\)	\(16\)
default	\(\frac {3 \,{\mathrm e} \ln \left (\ln \relax (6)+i \pi \right )}{x}\)	\(16\)
norman	\(\frac {3 \,{\mathrm e} \ln \left (\ln \relax (6)+i \pi \right )}{x}\)	\(16\)
risch	\(\frac {3 \,{\mathrm e} \ln \left (\ln \relax (2)+\ln \relax (3)+i \pi \right )}{x}\)	\(18\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-3*exp(1)*ln(ln(6)+I*Pi)/x^2,x,method=_RETURNVERBOSE)

[Out]

3*exp(1)/x*ln(ln(6)+I*Pi)

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maxima [A]  time = 0.35, size = 14, normalized size = 0.93 \begin {gather*} \frac {3 \, e \log \left (i \, \pi + \log \relax (6)\right )}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3*exp(1)*log(log(6)+I*pi)/x^2,x, algorithm="maxima")

[Out]

3*e*log(I*pi + log(6))/x

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mupad [B]  time = 5.82, size = 15, normalized size = 1.00 \begin {gather*} \frac {3\,\mathrm {e}\,\ln \left (\ln \relax (6)+\Pi \,1{}\mathrm {i}\right )}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(3*exp(1)*log(Pi*1i + log(6)))/x^2,x)

[Out]

(3*exp(1)*log(Pi*1i + log(6)))/x

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sympy [A]  time = 0.06, size = 14, normalized size = 0.93 \begin {gather*} \frac {3 e \log {\left (\log {\relax (6 )} + i \pi \right )}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-3*exp(1)*ln(ln(6)+I*pi)/x**2,x)

[Out]

3*E*log(log(6) + I*pi)/x

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