Optimal. Leaf size=22 \[ \log \left (\frac {x^2}{16 \left (2-\frac {x}{5}-x^2\right )^4}\right ) \]
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Rubi [A] time = 0.05, antiderivative size = 18, normalized size of antiderivative = 0.82, number of steps used = 4, number of rules used = 3, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.120, Rules used = {1594, 1628, 628} \begin {gather*} 2 \log (x)-4 \log \left (-5 x^2-x+10\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 628
Rule 1594
Rule 1628
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-20-2 x-30 x^2}{x \left (-10+x+5 x^2\right )} \, dx\\ &=\int \left (\frac {2}{x}-\frac {4 (1+10 x)}{-10+x+5 x^2}\right ) \, dx\\ &=2 \log (x)-4 \int \frac {1+10 x}{-10+x+5 x^2} \, dx\\ &=2 \log (x)-4 \log \left (10-x-5 x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 20, normalized size = 0.91 \begin {gather*} -2 \left (-\log (x)+2 \log \left (10-x-5 x^2\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 16, normalized size = 0.73 \begin {gather*} -4 \, \log \left (5 \, x^{2} + x - 10\right ) + 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.29, size = 18, normalized size = 0.82 \begin {gather*} -4 \, \log \left ({\left | 5 \, x^{2} + x - 10 \right |}\right ) + 2 \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 17, normalized size = 0.77
method | result | size |
default | \(2 \ln \relax (x )-4 \ln \left (5 x^{2}+x -10\right )\) | \(17\) |
norman | \(2 \ln \relax (x )-4 \ln \left (5 x^{2}+x -10\right )\) | \(17\) |
risch | \(2 \ln \relax (x )-4 \ln \left (5 x^{2}+x -10\right )\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 16, normalized size = 0.73 \begin {gather*} -4 \, \log \left (5 \, x^{2} + x - 10\right ) + 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.27, size = 16, normalized size = 0.73 \begin {gather*} 2\,\ln \relax (x)-4\,\ln \left (5\,x^2+x-10\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 15, normalized size = 0.68 \begin {gather*} 2 \log {\relax (x )} - 4 \log {\left (5 x^{2} + x - 10 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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