3.17.6 \(\int \frac {50 \log (6) \log (2 x)}{x} \, dx\)

Optimal. Leaf size=10 \[ 25 \log (6) \log ^2(2 x) \]

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Rubi [A]  time = 0.01, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {12, 2301} \begin {gather*} 25 \log (6) \log ^2(2 x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(50*Log[6]*Log[2*x])/x,x]

[Out]

25*Log[6]*Log[2*x]^2

Rule 12

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

Rule 2301

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))/(x_), x_Symbol] :> Simp[(a + b*Log[c*x^n])^2/(2*b*n), x] /; FreeQ[{a
, b, c, n}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=(50 \log (6)) \int \frac {\log (2 x)}{x} \, dx\\ &=25 \log (6) \log ^2(2 x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 10, normalized size = 1.00 \begin {gather*} 25 \log (6) \log ^2(2 x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(50*Log[6]*Log[2*x])/x,x]

[Out]

25*Log[6]*Log[2*x]^2

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fricas [A]  time = 0.72, size = 10, normalized size = 1.00 \begin {gather*} 25 \, \log \relax (6) \log \left (2 \, x\right )^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(50*log(6)*log(2*x)/x,x, algorithm="fricas")

[Out]

25*log(6)*log(2*x)^2

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giac [A]  time = 0.23, size = 10, normalized size = 1.00 \begin {gather*} 25 \, \log \relax (6) \log \left (2 \, x\right )^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(50*log(6)*log(2*x)/x,x, algorithm="giac")

[Out]

25*log(6)*log(2*x)^2

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maple [A]  time = 0.03, size = 11, normalized size = 1.10

method	result	size
derivativedivides	\(25 \ln \left (2 x \right )^{2} \ln \relax (6)\)	\(11\)
default	\(25 \ln \left (2 x \right )^{2} \ln \relax (6)\)	\(11\)
norman	\(25 \ln \left (2 x \right )^{2} \ln \relax (6)\)	\(11\)
risch	\(25 \ln \left (2 x \right )^{2} \ln \relax (2)+25 \ln \left (2 x \right )^{2} \ln \relax (3)\)	\(22\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(50*ln(6)*ln(2*x)/x,x,method=_RETURNVERBOSE)

[Out]

25*ln(2*x)^2*ln(6)

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maxima [A]  time = 0.53, size = 10, normalized size = 1.00 \begin {gather*} 25 \, \log \relax (6) \log \left (2 \, x\right )^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(50*log(6)*log(2*x)/x,x, algorithm="maxima")

[Out]

25*log(6)*log(2*x)^2

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mupad [B]  time = 1.03, size = 10, normalized size = 1.00 \begin {gather*} 25\,{\ln \left (2\,x\right )}^2\,\ln \relax (6) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((50*log(2*x)*log(6))/x,x)

[Out]

25*log(2*x)^2*log(6)

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sympy [A]  time = 0.10, size = 10, normalized size = 1.00 \begin {gather*} 25 \log {\relax (6 )} \log {\left (2 x \right )}^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(50*ln(6)*ln(2*x)/x,x)

[Out]

25*log(6)*log(2*x)**2

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