Optimal. Leaf size=14 \[ \frac {2 (b x)^{5/2}}{5 b} \]
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Rubi [A] time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {32} \[ \frac {2 (b x)^{5/2}}{5 b} \]
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin {align*} \int (b x)^{3/2} \, dx &=\frac {2 (b x)^{5/2}}{5 b}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 0.86 \[ \frac {2}{5} x (b x)^{3/2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 11, normalized size = 0.79 \[ \frac {2}{5} \, \sqrt {b x} b x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 11, normalized size = 0.79 \[ \frac {2}{5} \, \sqrt {b x} b x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 9, normalized size = 0.64 \[ \frac {2 \left (b x \right )^{\frac {3}{2}} x}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.31, size = 10, normalized size = 0.71 \[ \frac {2 \, \left (b x\right )^{\frac {5}{2}}}{5 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.01, size = 10, normalized size = 0.71 \[ \frac {2\,{\left (b\,x\right )}^{5/2}}{5\,b} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 10, normalized size = 0.71 \[ \frac {2 \left (b x\right )^{\frac {5}{2}}}{5 b} \]
Verification of antiderivative is not currently implemented for this CAS.
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