Optimal. Leaf size=21 \[ 5-x^2-\frac {5-x+\log (x)}{5 x^2} \]
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Rubi [A] time = 0.02, antiderivative size = 27, normalized size of antiderivative = 1.29, number of steps used = 6, number of rules used = 3, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 14, 2304} \begin {gather*} -x^2-\frac {1}{x^2}-\frac {\log (x)}{5 x^2}+\frac {1}{5 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2304
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {9-x-10 x^4+2 \log (x)}{x^3} \, dx\\ &=\frac {1}{5} \int \left (\frac {9-x-10 x^4}{x^3}+\frac {2 \log (x)}{x^3}\right ) \, dx\\ &=\frac {1}{5} \int \frac {9-x-10 x^4}{x^3} \, dx+\frac {2}{5} \int \frac {\log (x)}{x^3} \, dx\\ &=-\frac {1}{10 x^2}-\frac {\log (x)}{5 x^2}+\frac {1}{5} \int \left (\frac {9}{x^3}-\frac {1}{x^2}-10 x\right ) \, dx\\ &=-\frac {1}{x^2}+\frac {1}{5 x}-x^2-\frac {\log (x)}{5 x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 27, normalized size = 1.29 \begin {gather*} -\frac {1}{x^2}+\frac {1}{5 x}-x^2-\frac {\log (x)}{5 x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 17, normalized size = 0.81 \begin {gather*} -\frac {5 \, x^{4} - x + \log \relax (x) + 5}{5 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 21, normalized size = 1.00 \begin {gather*} -x^{2} + \frac {x - 5}{5 \, x^{2}} - \frac {\log \relax (x)}{5 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 19, normalized size = 0.90
method | result | size |
norman | \(\frac {-1+\frac {x}{5}-x^{4}-\frac {\ln \relax (x )}{5}}{x^{2}}\) | \(19\) |
default | \(-\frac {\ln \relax (x )}{5 x^{2}}-\frac {1}{x^{2}}-x^{2}+\frac {1}{5 x}\) | \(24\) |
risch | \(-\frac {\ln \relax (x )}{5 x^{2}}-\frac {5 x^{4}-x +5}{5 x^{2}}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 23, normalized size = 1.10 \begin {gather*} -x^{2} + \frac {1}{5 \, x} - \frac {\log \relax (x)}{5 \, x^{2}} - \frac {1}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.00, size = 20, normalized size = 0.95 \begin {gather*} -\frac {\frac {\ln \relax (x)}{5}-\frac {x}{5}+1}{x^2}-x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 20, normalized size = 0.95 \begin {gather*} - x^{2} - \frac {5 - x}{5 x^{2}} - \frac {\log {\relax (x )}}{5 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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