Optimal. Leaf size=32 \[ \frac {12}{\left (-4-x+\frac {1}{5} \left (-x+(5-5 x)^2 x^4\right )\right ) \log (x)} \]
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Rubi [F] time = 0.94, 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 {1200+360 x-1500 x^4+3000 x^5-1500 x^6+\left (360 x-6000 x^4+15000 x^5-9000 x^6\right ) \log (x)}{\left (400 x+240 x^2+36 x^3-1000 x^5+1700 x^6-400 x^7-300 x^8+625 x^9-2500 x^{10}+3750 x^{11}-2500 x^{12}+625 x^{13}\right ) \log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {60 \left (20+6 x-25 x^4+50 x^5-25 x^6-2 x \left (-3+50 x^3-125 x^4+75 x^5\right ) \log (x)\right )}{x \left (20+6 x-25 x^4+50 x^5-25 x^6\right )^2 \log ^2(x)} \, dx\\ &=60 \int \frac {20+6 x-25 x^4+50 x^5-25 x^6-2 x \left (-3+50 x^3-125 x^4+75 x^5\right ) \log (x)}{x \left (20+6 x-25 x^4+50 x^5-25 x^6\right )^2 \log ^2(x)} \, dx\\ &=60 \int \left (-\frac {1}{x \left (-20-6 x+25 x^4-50 x^5+25 x^6\right ) \log ^2(x)}-\frac {2 \left (-3+50 x^3-125 x^4+75 x^5\right )}{\left (-20-6 x+25 x^4-50 x^5+25 x^6\right )^2 \log (x)}\right ) \, dx\\ &=-\left (60 \int \frac {1}{x \left (-20-6 x+25 x^4-50 x^5+25 x^6\right ) \log ^2(x)} \, dx\right )-120 \int \frac {-3+50 x^3-125 x^4+75 x^5}{\left (-20-6 x+25 x^4-50 x^5+25 x^6\right )^2 \log (x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.34, size = 28, normalized size = 0.88 \begin {gather*} -\frac {60}{\left (20+6 x-25 x^4+50 x^5-25 x^6\right ) \log (x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 28, normalized size = 0.88 \begin {gather*} \frac {60}{{\left (25 \, x^{6} - 50 \, x^{5} + 25 \, x^{4} - 6 \, x - 20\right )} \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 35, normalized size = 1.09 \begin {gather*} \frac {60}{25 \, x^{6} \log \relax (x) - 50 \, x^{5} \log \relax (x) + 25 \, x^{4} \log \relax (x) - 6 \, x \log \relax (x) - 20 \, \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 29, normalized size = 0.91
method | result | size |
risch | \(\frac {60}{\left (25 x^{6}-50 x^{5}+25 x^{4}-6 x -20\right ) \ln \relax (x )}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.65, size = 28, normalized size = 0.88 \begin {gather*} \frac {60}{{\left (25 \, x^{6} - 50 \, x^{5} + 25 \, x^{4} - 6 \, x - 20\right )} \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.75, size = 28, normalized size = 0.88 \begin {gather*} -\frac {60}{\ln \relax (x)\,\left (-25\,x^6+50\,x^5-25\,x^4+6\,x+20\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 24, normalized size = 0.75 \begin {gather*} \frac {60}{\left (25 x^{6} - 50 x^{5} + 25 x^{4} - 6 x - 20\right ) \log {\relax (x )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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