3.83.42 \(\int \frac {-30 x+(-5-x) \log (4)+6 x^2 \log (x)}{-5 x+x^2 \log (x)} \, dx\)

Optimal. Leaf size=19 \[ 6 x-\log (4) \log \left (\frac {5}{x}-\log (x)\right ) \]

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Rubi [F]  time = 0.47, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {-30 x+(-5-x) \log (4)+6 x^2 \log (x)}{-5 x+x^2 \log (x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-30*x + (-5 - x)*Log[4] + 6*x^2*Log[x])/(-5*x + x^2*Log[x]),x]

[Out]

6*x - Log[4]*Defer[Int][(-5 + x*Log[x])^(-1), x] - 5*Log[4]*Defer[Int][1/(x*(-5 + x*Log[x])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-30 x+(-5-x) \log (4)+6 x^2 \log (x)}{x^2 \left (-\frac {5}{x}+\log (x)\right )} \, dx\\ &=\int \frac {-30 x+(-5-x) \log (4)+6 x^2 \log (x)}{x (-5+x \log (x))} \, dx\\ &=\int \left (6-\frac {(5+x) \log (4)}{x (-5+x \log (x))}\right ) \, dx\\ &=6 x-\log (4) \int \frac {5+x}{x (-5+x \log (x))} \, dx\\ &=6 x-\log (4) \int \left (\frac {1}{-5+x \log (x)}+\frac {5}{x (-5+x \log (x))}\right ) \, dx\\ &=6 x-\log (4) \int \frac {1}{-5+x \log (x)} \, dx-(5 \log (4)) \int \frac {1}{x (-5+x \log (x))} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.07, size = 21, normalized size = 1.11 \begin {gather*} 6 x+\log (4) \log (x)-\log (4) \log (5-x \log (x)) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-30*x + (-5 - x)*Log[4] + 6*x^2*Log[x])/(-5*x + x^2*Log[x]),x]

[Out]

6*x + Log[4]*Log[x] - Log[4]*Log[5 - x*Log[x]]

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fricas [A]  time = 1.04, size = 19, normalized size = 1.00 \begin {gather*} -2 \, \log \relax (2) \log \left (\frac {x \log \relax (x) - 5}{x}\right ) + 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((6*x^2*log(x)+2*(-x-5)*log(2)-30*x)/(x^2*log(x)-5*x),x, algorithm="fricas")

[Out]

-2*log(2)*log((x*log(x) - 5)/x) + 6*x

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giac [A]  time = 0.12, size = 21, normalized size = 1.11 \begin {gather*} -2 \, \log \relax (2) \log \left (x \log \relax (x) - 5\right ) + 2 \, \log \relax (2) \log \relax (x) + 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((6*x^2*log(x)+2*(-x-5)*log(2)-30*x)/(x^2*log(x)-5*x),x, algorithm="giac")

[Out]

-2*log(2)*log(x*log(x) - 5) + 2*log(2)*log(x) + 6*x

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maple [A]  time = 0.05, size = 18, normalized size = 0.95

method	result	size
risch	\(6 x -2 \ln \relax (2) \ln \left (\ln \relax (x )-\frac {5}{x}\right )\)	\(18\)
default	\(6 x +2 \ln \relax (2) \ln \relax (x )-2 \ln \relax (2) \ln \left (x \ln \relax (x )-5\right )\)	\(22\)
norman	\(6 x +2 \ln \relax (2) \ln \relax (x )-2 \ln \relax (2) \ln \left (x \ln \relax (x )-5\right )\)	\(22\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((6*x^2*ln(x)+2*(-x-5)*ln(2)-30*x)/(x^2*ln(x)-5*x),x,method=_RETURNVERBOSE)

[Out]

6*x-2*ln(2)*ln(ln(x)-5/x)

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maxima [A]  time = 0.49, size = 19, normalized size = 1.00 \begin {gather*} -2 \, \log \relax (2) \log \left (\frac {x \log \relax (x) - 5}{x}\right ) + 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((6*x^2*log(x)+2*(-x-5)*log(2)-30*x)/(x^2*log(x)-5*x),x, algorithm="maxima")

[Out]

-2*log(2)*log((x*log(x) - 5)/x) + 6*x

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mupad [B]  time = 4.89, size = 21, normalized size = 1.11 \begin {gather*} 6\,x-2\,\ln \relax (2)\,\ln \left (x\,\ln \relax (x)-5\right )+2\,\ln \relax (2)\,\ln \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((30*x - 6*x^2*log(x) + 2*log(2)*(x + 5))/(5*x - x^2*log(x)),x)

[Out]

6*x - 2*log(2)*log(x*log(x) - 5) + 2*log(2)*log(x)

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sympy [A]  time = 0.15, size = 15, normalized size = 0.79 \begin {gather*} 6 x - 2 \log {\relax (2 )} \log {\left (\log {\relax (x )} - \frac {5}{x} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((6*x**2*ln(x)+2*(-x-5)*ln(2)-30*x)/(x**2*ln(x)-5*x),x)

[Out]

6*x - 2*log(2)*log(log(x) - 5/x)

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