Optimal. Leaf size=17 \[ \frac {2}{11} b x^4 \sqrt {b x^3} \]
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Rubi [A] time = 0.00, antiderivative size = 17, 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} \[ \frac {2}{11} b x^4 \sqrt {b x^3} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \left (b x^3\right )^{3/2} \, dx &=\frac {\left (b \sqrt {b x^3}\right ) \int x^{9/2} \, dx}{x^{3/2}}\\ &=\frac {2}{11} b x^4 \sqrt {b x^3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 0.82 \[ \frac {2}{11} x \left (b x^3\right )^{3/2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.86, size = 13, normalized size = 0.76 \[ \frac {2}{11} \, \sqrt {b x^{3}} b x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 13, normalized size = 0.76 \[ \frac {2}{11} \, \sqrt {b x} b x^{5} \mathrm {sgn}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 11, normalized size = 0.65 \[ \frac {2 \left (b \,x^{3}\right )^{\frac {3}{2}} x}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.29, size = 10, normalized size = 0.59 \[ \frac {2}{11} \, \left (b x^{3}\right )^{\frac {3}{2}} x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.95, size = 10, normalized size = 0.59 \[ \frac {2\,x\,{\left (b\,x^3\right )}^{3/2}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.39, size = 15, normalized size = 0.88 \[ \frac {2 b^{\frac {3}{2}} x \left (x^{3}\right )^{\frac {3}{2}}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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