Optimal. Leaf size=17 \[ \frac {1}{5} \left (\frac {2}{x^2}-\frac {174 x}{5}+\log (x)\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 19, normalized size of antiderivative = 1.12, number of steps used = 3, number of rules used = 2, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {12, 14} \begin {gather*} \frac {2}{5 x^2}-\frac {174 x}{25}+\frac {\log (x)}{5} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{25} \int \frac {-20+5 x^2-174 x^3}{x^3} \, dx\\ &=\frac {1}{25} \int \left (-174-\frac {20}{x^3}+\frac {5}{x}\right ) \, dx\\ &=\frac {2}{5 x^2}-\frac {174 x}{25}+\frac {\log (x)}{5}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} \frac {1}{25} \left (\frac {10}{x^2}-174 x+5 \log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 19, normalized size = 1.12 \begin {gather*} -\frac {174 \, x^{3} - 5 \, x^{2} \log \relax (x) - 10}{25 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 14, normalized size = 0.82 \begin {gather*} -\frac {174}{25} \, x + \frac {2}{5 \, x^{2}} + \frac {1}{5} \, \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 = 14, normalized size = 0.82
method | result | size |
default | \(-\frac {174 x}{25}+\frac {2}{5 x^{2}}+\frac {\ln \relax (x )}{5}\) | \(14\) |
risch | \(-\frac {174 x}{25}+\frac {2}{5 x^{2}}+\frac {\ln \relax (x )}{5}\) | \(14\) |
norman | \(\frac {\frac {2}{5}-\frac {174 x^{3}}{25}}{x^{2}}+\frac {\ln \relax (x )}{5}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 13, normalized size = 0.76 \begin {gather*} -\frac {174}{25} \, x + \frac {2}{5 \, x^{2}} + \frac {1}{5} \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 13, normalized size = 0.76 \begin {gather*} \frac {\ln \relax (x)}{5}-\frac {174\,x}{25}+\frac {2}{5\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 15, normalized size = 0.88 \begin {gather*} - \frac {174 x}{25} + \frac {\log {\relax (x )}}{5} + \frac {2}{5 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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