Optimal. Leaf size=29 \[ 1-x+5 (4+x)+\log (x)-\frac {3-x}{-10 x+\log ^2(x)} \]
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Rubi [F] time = 0.68, 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+100 x^2+400 x^3+(6-2 x) \log (x)+\left (-19 x-80 x^2\right ) \log ^2(x)+(1+4 x) \log ^4(x)}{100 x^3-20 x^2 \log ^2(x)+x \log ^4(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 {-30 x+100 x^2+400 x^3+(6-2 x) \log (x)+\left (-19 x-80 x^2\right ) \log ^2(x)+(1+4 x) \log ^4(x)}{x \left (10 x-\log ^2(x)\right )^2} \, dx\\ &=\int \left (\frac {1+4 x}{x}+\frac {2 (-3+x) (5 x-\log (x))}{x \left (10 x-\log ^2(x)\right )^2}+\frac {1}{-10 x+\log ^2(x)}\right ) \, dx\\ &=2 \int \frac {(-3+x) (5 x-\log (x))}{x \left (10 x-\log ^2(x)\right )^2} \, dx+\int \frac {1+4 x}{x} \, dx+\int \frac {1}{-10 x+\log ^2(x)} \, dx\\ &=2 \int \left (\frac {5 x-\log (x)}{\left (10 x-\log ^2(x)\right )^2}-\frac {3 (5 x-\log (x))}{x \left (10 x-\log ^2(x)\right )^2}\right ) \, dx+\int \left (4+\frac {1}{x}\right ) \, dx+\int \frac {1}{-10 x+\log ^2(x)} \, dx\\ &=4 x+\log (x)+2 \int \frac {5 x-\log (x)}{\left (10 x-\log ^2(x)\right )^2} \, dx-6 \int \frac {5 x-\log (x)}{x \left (10 x-\log ^2(x)\right )^2} \, dx+\int \frac {1}{-10 x+\log ^2(x)} \, dx\\ &=4 x+\log (x)+\frac {3}{10 x-\log ^2(x)}+2 \int \left (\frac {5 x}{\left (10 x-\log ^2(x)\right )^2}-\frac {\log (x)}{\left (-10 x+\log ^2(x)\right )^2}\right ) \, dx+\int \frac {1}{-10 x+\log ^2(x)} \, dx\\ &=4 x+\log (x)+\frac {3}{10 x-\log ^2(x)}-2 \int \frac {\log (x)}{\left (-10 x+\log ^2(x)\right )^2} \, dx+10 \int \frac {x}{\left (10 x-\log ^2(x)\right )^2} \, dx+\int \frac {1}{-10 x+\log ^2(x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.18, size = 20, normalized size = 0.69 \begin {gather*} 4 x+\log (x)+\frac {-3+x}{-10 x+\log ^2(x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 2.14, size = 35, normalized size = 1.21 \begin {gather*} \frac {4 \, x \log \relax (x)^{2} + \log \relax (x)^{3} - 40 \, x^{2} - 10 \, x \log \relax (x) + x - 3}{\log \relax (x)^{2} - 10 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 20, normalized size = 0.69 \begin {gather*} 4 \, x + \frac {x - 3}{\log \relax (x)^{2} - 10 \, x} + \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 = 24, normalized size = 0.83
method | result | size |
risch | \(4 x +\ln \relax (x )-\frac {x -3}{-\ln \relax (x )^{2}+10 x}\) | \(24\) |
norman | \(\frac {3-\frac {\ln \relax (x )^{2}}{10}+40 x^{2}-4 x \ln \relax (x )^{2}}{-\ln \relax (x )^{2}+10 x}+\ln \relax (x )\) | \(37\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 29, normalized size = 1.00 \begin {gather*} \frac {4 \, x \log \relax (x)^{2} - 40 \, x^{2} + x - 3}{\log \relax (x)^{2} - 10 \, x} + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.36, size = 23, normalized size = 0.79 \begin {gather*} 4\,x+\ln \relax (x)-\frac {x-3}{10\,x-{\ln \relax (x)}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 17, normalized size = 0.59 \begin {gather*} 4 x + \log {\relax (x )} + \frac {x - 3}{- 10 x + \log {\relax (x )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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