Optimal. Leaf size=17 \[ -\frac {2}{3 n \log ^{\frac {3}{2}}\left (a x^n\right )} \]
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Rubi [A] time = 0.01, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {2302, 30} \[ -\frac {2}{3 n \log ^{\frac {3}{2}}\left (a x^n\right )} \]
Antiderivative was successfully verified.
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Rule 30
Rule 2302
Rubi steps
\begin {align*} \int \frac {1}{x \log ^{\frac {5}{2}}\left (a x^n\right )} \, dx &=\frac {\operatorname {Subst}\left (\int \frac {1}{x^{5/2}} \, dx,x,\log \left (a x^n\right )\right )}{n}\\ &=-\frac {2}{3 n \log ^{\frac {3}{2}}\left (a x^n\right )}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \[ -\frac {2}{3 n \log ^{\frac {3}{2}}\left (a x^n\right )} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.45, size = 37, normalized size = 2.18 \[ -\frac {2 \, \sqrt {n \log \relax (x) + \log \relax (a)}}{3 \, {\left (n^{3} \log \relax (x)^{2} + 2 \, n^{2} \log \relax (a) \log \relax (x) + n \log \relax (a)^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.25, size = 14, normalized size = 0.82 \[ -\frac {2}{3 \, {\left (n \log \relax (x) + \log \relax (a)\right )}^{\frac {3}{2}} n} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 14, normalized size = 0.82 \[ -\frac {2}{3 n \ln \left (a \,x^{n}\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.81, size = 13, normalized size = 0.76 \[ -\frac {2}{3 \, n \log \left (a x^{n}\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.43, size = 13, normalized size = 0.76 \[ -\frac {2}{3\,n\,{\ln \left (a\,x^n\right )}^{3/2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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