Optimal. Leaf size=34 \[ -\frac {16}{27 x^{3/2}}-\frac {2 \log ^2(x)}{3 x^{3/2}}-\frac {8 \log (x)}{9 x^{3/2}} \]
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Rubi [A] time = 0.02, antiderivative size = 34, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {2305, 2304} \[ -\frac {16}{27 x^{3/2}}-\frac {2 \log ^2(x)}{3 x^{3/2}}-\frac {8 \log (x)}{9 x^{3/2}} \]
Antiderivative was successfully verified.
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Rule 2304
Rule 2305
Rubi steps
\begin {align*} \int \frac {\log ^2(x)}{x^{5/2}} \, dx &=-\frac {2 \log ^2(x)}{3 x^{3/2}}+\frac {4}{3} \int \frac {\log (x)}{x^{5/2}} \, dx\\ &=-\frac {16}{27 x^{3/2}}-\frac {8 \log (x)}{9 x^{3/2}}-\frac {2 \log ^2(x)}{3 x^{3/2}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 21, normalized size = 0.62 \[ -\frac {2 \left (9 \log ^2(x)+12 \log (x)+8\right )}{27 x^{3/2}} \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\log ^2(x)}{x^{5/2}} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 1.16, size = 17, normalized size = 0.50 \[ -\frac {2 \, {\left (9 \, \log \relax (x)^{2} + 12 \, \log \relax (x) + 8\right )}}{27 \, x^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.63, size = 22, normalized size = 0.65 \[ -\frac {2 \, \log \relax (x)^{2}}{3 \, x^{\frac {3}{2}}} - \frac {8 \, \log \relax (x)}{9 \, x^{\frac {3}{2}}} - \frac {16}{27 \, x^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.10, size = 23, normalized size = 0.68
method | result | size |
derivativedivides | \(-\frac {16}{27 x^{\frac {3}{2}}}-\frac {8 \ln \relax (x )}{9 x^{\frac {3}{2}}}-\frac {2 \ln \relax (x )^{2}}{3 x^{\frac {3}{2}}}\) | \(23\) |
default | \(-\frac {16}{27 x^{\frac {3}{2}}}-\frac {8 \ln \relax (x )}{9 x^{\frac {3}{2}}}-\frac {2 \ln \relax (x )^{2}}{3 x^{\frac {3}{2}}}\) | \(23\) |
risch | \(-\frac {16}{27 x^{\frac {3}{2}}}-\frac {8 \ln \relax (x )}{9 x^{\frac {3}{2}}}-\frac {2 \ln \relax (x )^{2}}{3 x^{\frac {3}{2}}}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 22, normalized size = 0.65 \[ -\frac {2 \, \log \relax (x)^{2}}{3 \, x^{\frac {3}{2}}} - \frac {8 \, \log \relax (x)}{9 \, x^{\frac {3}{2}}} - \frac {16}{27 \, x^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 17, normalized size = 0.50 \[ -\frac {18\,{\ln \relax (x)}^2+24\,\ln \relax (x)+16}{27\,x^{3/2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 6.09, size = 34, normalized size = 1.00 \[ - \frac {2 \log {\relax (x )}^{2}}{3 x^{\frac {3}{2}}} - \frac {8 \log {\relax (x )}}{9 x^{\frac {3}{2}}} - \frac {16}{27 x^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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