Optimal. Leaf size=23 \[ \frac {-3+\frac {x}{2}}{(-10+x) \left (5 x^2+\log (x)\right )} \]
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Rubi [F]
time = 0.90, 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 {-60+16 x-601 x^2+140 x^3-10 x^4-4 x \log (x)}{5000 x^5-1000 x^6+50 x^7+\left (2000 x^3-400 x^4+20 x^5\right ) \log (x)+\left (200 x-40 x^2+2 x^3\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+16 x-601 x^2+140 x^3-10 x^4-4 x \log (x)}{2 (10-x)^2 x \left (5 x^2+\log (x)\right )^2} \, dx\\ &=\frac {1}{2} \int \frac {-60+16 x-601 x^2+140 x^3-10 x^4-4 x \log (x)}{(10-x)^2 x \left (5 x^2+\log (x)\right )^2} \, dx\\ &=\frac {1}{2} \int \left (\frac {6-x+60 x^2-10 x^3}{(-10+x) x \left (5 x^2+\log (x)\right )^2}-\frac {4}{(-10+x)^2 \left (5 x^2+\log (x)\right )}\right ) \, dx\\ &=\frac {1}{2} \int \frac {6-x+60 x^2-10 x^3}{(-10+x) x \left (5 x^2+\log (x)\right )^2} \, dx-2 \int \frac {1}{(-10+x)^2 \left (5 x^2+\log (x)\right )} \, dx\\ &=\frac {1}{2} \int \left (-\frac {40}{\left (5 x^2+\log (x)\right )^2}-\frac {2002}{5 (-10+x) \left (5 x^2+\log (x)\right )^2}-\frac {3}{5 x \left (5 x^2+\log (x)\right )^2}-\frac {10 x}{\left (5 x^2+\log (x)\right )^2}\right ) \, dx-2 \int \frac {1}{(-10+x)^2 \left (5 x^2+\log (x)\right )} \, dx\\ &=-\left (\frac {3}{10} \int \frac {1}{x \left (5 x^2+\log (x)\right )^2} \, dx\right )-2 \int \frac {1}{(-10+x)^2 \left (5 x^2+\log (x)\right )} \, dx-5 \int \frac {x}{\left (5 x^2+\log (x)\right )^2} \, dx-20 \int \frac {1}{\left (5 x^2+\log (x)\right )^2} \, dx-\frac {1001}{5} \int \frac {1}{(-10+x) \left (5 x^2+\log (x)\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.38, size = 24, normalized size = 1.04 \begin {gather*} -\frac {6-x}{2 (-10+x) \left (5 x^2+\log (x)\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.24, size = 23, normalized size = 1.00
method | result | size |
risch | \(\frac {x -6}{2 \left (x -10\right ) \left (5 x^{2}+\ln \left (x \right )\right )}\) | \(21\) |
default | \(-\frac {-x +6}{2 \left (x -10\right ) \left (5 x^{2}+\ln \left (x \right )\right )}\) | \(23\) |
norman | \(\frac {\frac {x}{2}-3}{5 x^{3}+x \ln \left (x \right )-50 x^{2}-10 \ln \left (x \right )}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 24, normalized size = 1.04 \begin {gather*} \frac {x - 6}{2 \, {\left (5 \, x^{3} - 50 \, x^{2} + {\left (x - 10\right )} \log \left (x\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 24, normalized size = 1.04 \begin {gather*} \frac {x - 6}{2 \, {\left (5 \, x^{3} - 50 \, x^{2} + {\left (x - 10\right )} \log \left (x\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 20, normalized size = 0.87 \begin {gather*} \frac {x - 6}{10 x^{3} - 100 x^{2} + \left (2 x - 20\right ) \log {\left (x \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 26, normalized size = 1.13 \begin {gather*} \frac {x - 6}{2 \, {\left (5 \, x^{3} - 50 \, x^{2} + x \log \left (x\right ) - 10 \, \log \left (x\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 6.49, size = 20, normalized size = 0.87 \begin {gather*} \frac {x-6}{2\,\left (\ln \left (x\right )+5\,x^2\right )\,\left (x-10\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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