3.101.80 \(\int \frac {-2+44 x+2 \log (x^2)}{-3 x+11 x^2+x \log (x^2)} \, dx\)

Optimal. Leaf size=21 \[ \log \left (\left (-4 x^2+2 x \left (-3+13 x+\log \left (x^2\right )\right )\right )^2\right ) \]

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Rubi [A]  time = 0.03, antiderivative size = 19, normalized size of antiderivative = 0.90, number of steps used = 1, number of rules used = 1, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.034, Rules used = {6684} \begin {gather*} 2 \log \left (-11 x^2-x \log \left (x^2\right )+3 x\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-2 + 44*x + 2*Log[x^2])/(-3*x + 11*x^2 + x*Log[x^2]),x]

[Out]

2*Log[3*x - 11*x^2 - x*Log[x^2]]

Rule 6684

Int[(u_)/(y_), x_Symbol] :> With[{q = DerivativeDivides[y, u, x]}, Simp[q*Log[RemoveContent[y, x]], x] /;  !Fa
lseQ[q]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=2 \log \left (3 x-11 x^2-x \log \left (x^2\right )\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.11, size = 17, normalized size = 0.81 \begin {gather*} 2 \left (\log (x)+\log \left (3-11 x-\log \left (x^2\right )\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-2 + 44*x + 2*Log[x^2])/(-3*x + 11*x^2 + x*Log[x^2]),x]

[Out]

2*(Log[x] + Log[3 - 11*x - Log[x^2]])

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fricas [A]  time = 0.65, size = 17, normalized size = 0.81 \begin {gather*} \log \left (x^{2}\right ) + 2 \, \log \left (11 \, x + \log \left (x^{2}\right ) - 3\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*log(x^2)+44*x-2)/(x*log(x^2)+11*x^2-3*x),x, algorithm="fricas")

[Out]

log(x^2) + 2*log(11*x + log(x^2) - 3)

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giac [A]  time = 0.16, size = 17, normalized size = 0.81 \begin {gather*} 2 \, \log \left (11 \, x + \log \left (x^{2}\right ) - 3\right ) + 2 \, \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*log(x^2)+44*x-2)/(x*log(x^2)+11*x^2-3*x),x, algorithm="giac")

[Out]

2*log(11*x + log(x^2) - 3) + 2*log(x)

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maple [A]  time = 0.02, size = 18, normalized size = 0.86

method	result	size
norman	\(2 \ln \relax (x )+2 \ln \left (11 x -3+\ln \left (x^{2}\right )\right )\)	\(18\)
risch	\(2 \ln \relax (x )+2 \ln \left (11 x -3+\ln \left (x^{2}\right )\right )\)	\(18\)
default	\(2 \ln \left (x \ln \left (x^{2}\right )+11 x^{2}-3 x \right )\)	\(19\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*ln(x^2)+44*x-2)/(x*ln(x^2)+11*x^2-3*x),x,method=_RETURNVERBOSE)

[Out]

2*ln(x)+2*ln(11*x-3+ln(x^2))

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maxima [A]  time = 0.35, size = 18, normalized size = 0.86 \begin {gather*} 2 \, \log \left (11 \, x^{2} + x \log \left (x^{2}\right ) - 3 \, x\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*log(x^2)+44*x-2)/(x*log(x^2)+11*x^2-3*x),x, algorithm="maxima")

[Out]

2*log(11*x^2 + x*log(x^2) - 3*x)

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mupad [B]  time = 6.06, size = 17, normalized size = 0.81 \begin {gather*} \ln \left (x^2\right )+2\,\ln \left (11\,x+\ln \left (x^2\right )-3\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((44*x + 2*log(x^2) - 2)/(x*log(x^2) - 3*x + 11*x^2),x)

[Out]

log(x^2) + 2*log(11*x + log(x^2) - 3)

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sympy [A]  time = 0.14, size = 17, normalized size = 0.81 \begin {gather*} 2 \log {\relax (x )} + 2 \log {\left (11 x + \log {\left (x^{2} \right )} - 3 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*ln(x**2)+44*x-2)/(x*ln(x**2)+11*x**2-3*x),x)

[Out]

2*log(x) + 2*log(11*x + log(x**2) - 3)

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