3.95.41 \(\int -\frac {8 \log ^2(2)}{x} \, dx\)

Optimal. Leaf size=15 \[ -3+4 \log ^2(2) \log \left (\frac {\log (3)}{x^2}\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 8, normalized size of antiderivative = 0.53, 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, 29} \begin {gather*} -8 \log ^2(2) \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-8*Log[2]^2)/x,x]

[Out]

-8*Log[2]^2*Log[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 29

Int[(x_)^(-1), x_Symbol] :> Simp[Log[x], x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\left (\left (8 \log ^2(2)\right ) \int \frac {1}{x} \, dx\right )\\ &=-8 \log ^2(2) \log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 8, normalized size = 0.53 \begin {gather*} -8 \log ^2(2) \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-8*Log[2]^2)/x,x]

[Out]

-8*Log[2]^2*Log[x]

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fricas [A]  time = 0.60, size = 8, normalized size = 0.53 \begin {gather*} -8 \, \log \relax (2)^{2} \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8*log(2)^2/x,x, algorithm="fricas")

[Out]

-8*log(2)^2*log(x)

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giac [A]  time = 0.21, size = 9, normalized size = 0.60 \begin {gather*} -8 \, \log \relax (2)^{2} \log \left ({\left | x \right |}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8*log(2)^2/x,x, algorithm="giac")

[Out]

-8*log(2)^2*log(abs(x))

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maple [A]  time = 0.03, size = 9, normalized size = 0.60

method	result	size
default	\(-8 \ln \relax (x ) \ln \relax (2)^{2}\)	\(9\)
norman	\(-8 \ln \relax (x ) \ln \relax (2)^{2}\)	\(9\)
risch	\(-8 \ln \relax (x ) \ln \relax (2)^{2}\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-8*ln(2)^2/x,x,method=_RETURNVERBOSE)

[Out]

-8*ln(x)*ln(2)^2

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maxima [A]  time = 0.34, size = 8, normalized size = 0.53 \begin {gather*} -8 \, \log \relax (2)^{2} \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8*log(2)^2/x,x, algorithm="maxima")

[Out]

-8*log(2)^2*log(x)

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mupad [B]  time = 7.63, size = 8, normalized size = 0.53 \begin {gather*} -8\,{\ln \relax (2)}^2\,\ln \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(8*log(2)^2)/x,x)

[Out]

-8*log(2)^2*log(x)

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sympy [A]  time = 0.05, size = 10, normalized size = 0.67 \begin {gather*} - 8 \log {\relax (2 )}^{2} \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8*ln(2)**2/x,x)

[Out]

-8*log(2)**2*log(x)

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