Optimal. Leaf size=19 \[ \frac {x^3}{4 b \sqrt {\frac {b}{x^2}}} \]
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Rubi [A] time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {15, 30} \[ \frac {x^3}{4 b \sqrt {\frac {b}{x^2}}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {1}{\left (\frac {b}{x^2}\right )^{3/2}} \, dx &=\frac {\int x^3 \, dx}{b \sqrt {\frac {b}{x^2}} x}\\ &=\frac {x^3}{4 b \sqrt {\frac {b}{x^2}}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 0.74 \[ \frac {x}{4 \left (\frac {b}{x^2}\right )^{3/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 15, normalized size = 0.79 \[ \frac {x^{5} \sqrt {\frac {b}{x^{2}}}}{4 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 8, normalized size = 0.42 \[ \frac {x^{4}}{4 \, b^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 11, normalized size = 0.58 \[ \frac {x}{4 \left (\frac {b}{x^{2}}\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.32, size = 10, normalized size = 0.53 \[ \frac {x}{4 \, \left (\frac {b}{x^{2}}\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.93, size = 13, normalized size = 0.68 \[ \frac {x^5\,\sqrt {\frac {1}{x^2}}}{4\,b^{3/2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.51, size = 15, normalized size = 0.79 \[ \frac {x}{4 b^{\frac {3}{2}} \left (\frac {1}{x^{2}}\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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