Optimal. Leaf size=16 \[ \frac {x \log (x)}{b^2 \sqrt {b x^2}} \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {15, 29} \[ \frac {x \log (x)}{b^2 \sqrt {b x^2}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 29
Rubi steps
\begin {align*} \int \frac {x^4}{\left (b x^2\right )^{5/2}} \, dx &=\frac {x \int \frac {1}{x} \, dx}{b^2 \sqrt {b x^2}}\\ &=\frac {x \log (x)}{b^2 \sqrt {b x^2}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 0.94 \[ \frac {x^5 \log (x)}{\left (b x^2\right )^{5/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 16, normalized size = 1.00 \[ \frac {\sqrt {b x^{2}} \log \relax (x)}{b^{3} x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 21, normalized size = 1.31 \[ -\frac {\log \left ({\left | -\sqrt {b} x + \sqrt {b x^{2}} \right |}\right )}{b^{\frac {5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 0.88 \[ \frac {x^{5} \ln \relax (x )}{\left (b \,x^{2}\right )^{\frac {5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.34, size = 6, normalized size = 0.38 \[ \frac {\log \relax (x)}{b^{\frac {5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.06 \[ \int \frac {x^4}{{\left (b\,x^2\right )}^{5/2}} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x^{4}}{\left (b x^{2}\right )^{\frac {5}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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