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

Optimal. Leaf size=10 $$25\log (6){\log }^2(2x)$$

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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} $$\begin{array}{c}25\log (6){\log }^2(2x)\end{array}$$

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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =(50\log (6))\int \frac{\log (2x)}{x}dx\\ & =25\log (6){\log }^2(2x)\end{array}\end{array}$$

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

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 $$\begin{array}{c}25\log (6)\log {\left(2x\right)}^2\end{array}$$

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 $$\begin{array}{c}25\log (6)\log {\left(2x\right)}^2\end{array}$$

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	$25\ln {\left(2x\right)}^2\ln (6)$	$11$
default	$25\ln {\left(2x\right)}^2\ln (6)$	$11$
norman	$25\ln {\left(2x\right)}^2\ln (6)$	$11$
risch	$25\ln {\left(2x\right)}^2\ln (2)+25\ln {\left(2x\right)}^2\ln (3)$	$22$

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 $$\begin{array}{c}25\log (6)\log {\left(2x\right)}^2\end{array}$$

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 $$\begin{array}{c}25{\ln \left(2x\right)}^2\ln (6)\end{array}$$

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 $$\begin{array}{c}25\log (6)\log {\left(2x\right)}^2\end{array}$$

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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