Optimal. Leaf size=28 \[ -5+x+\frac {(2 (-2+x)-625 x) \left (x+\frac {1-\log (x)}{x}\right )}{x} \]
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Rubi [A] time = 0.05, antiderivative size = 36, normalized size of antiderivative = 1.29, number of steps used = 8, number of rules used = 5, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.227, Rules used = {14, 37, 2334, 12, 43} \begin {gather*} -\frac {4}{x^2}+\frac {(623 x+8)^2 \log (x)}{16 x^2}-622 x-\frac {623}{x}-\frac {388129 \log (x)}{16} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 37
Rule 43
Rule 2334
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {2 \left (-6-623 x+311 x^3\right )}{x^3}-\frac {(8+623 x) \log (x)}{x^3}\right ) \, dx\\ &=-\left (2 \int \frac {-6-623 x+311 x^3}{x^3} \, dx\right )-\int \frac {(8+623 x) \log (x)}{x^3} \, dx\\ &=\frac {(8+623 x)^2 \log (x)}{16 x^2}-2 \int \left (311-\frac {6}{x^3}-\frac {623}{x^2}\right ) \, dx+\int -\frac {(8+623 x)^2}{16 x^3} \, dx\\ &=-\frac {6}{x^2}-\frac {1246}{x}-622 x+\frac {(8+623 x)^2 \log (x)}{16 x^2}-\frac {1}{16} \int \frac {(8+623 x)^2}{x^3} \, dx\\ &=-\frac {6}{x^2}-\frac {1246}{x}-622 x+\frac {(8+623 x)^2 \log (x)}{16 x^2}-\frac {1}{16} \int \left (\frac {64}{x^3}+\frac {9968}{x^2}+\frac {388129}{x}\right ) \, dx\\ &=-\frac {4}{x^2}-\frac {623}{x}-622 x-\frac {388129 \log (x)}{16}+\frac {(8+623 x)^2 \log (x)}{16 x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 28, normalized size = 1.00 \begin {gather*} -\frac {4}{x^2}-\frac {623}{x}-622 x+\frac {4 \log (x)}{x^2}+\frac {623 \log (x)}{x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.56, size = 24, normalized size = 0.86 \begin {gather*} -\frac {622 \, x^{3} - {\left (623 \, x + 4\right )} \log \relax (x) + 623 \, x + 4}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 25, normalized size = 0.89 \begin {gather*} -622 \, x + \frac {{\left (623 \, x + 4\right )} \log \relax (x)}{x^{2}} - \frac {623 \, x + 4}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 24, normalized size = 0.86
method | result | size |
norman | \(\frac {-4-623 x -622 x^{3}+623 x \ln \relax (x )+4 \ln \relax (x )}{x^{2}}\) | \(24\) |
risch | \(\frac {\left (623 x +4\right ) \ln \relax (x )}{x^{2}}-\frac {622 x^{3}+623 x +4}{x^{2}}\) | \(28\) |
default | \(-622 x +\frac {623 \ln \relax (x )}{x}-\frac {623}{x}+\frac {4 \ln \relax (x )}{x^{2}}-\frac {4}{x^{2}}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 28, normalized size = 1.00 \begin {gather*} -622 \, x + \frac {623 \, \log \relax (x)}{x} - \frac {623}{x} + \frac {4 \, \log \relax (x)}{x^{2}} - \frac {4}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.06, size = 27, normalized size = 0.96 \begin {gather*} \frac {x\,\left (4\,\ln \relax (x)-4\right )+x^2\,\left (623\,\ln \relax (x)-623\right )}{x^3}-622\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 22, normalized size = 0.79 \begin {gather*} - 622 x + \frac {\left (623 x + 4\right ) \log {\relax (x )}}{x^{2}} - \frac {623 x + 4}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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