Optimal. Leaf size=17 \[ \frac {1}{4} b x^3 \sqrt {b x^2} \]
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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} \[ \frac {1}{4} b x^3 \sqrt {b x^2} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \left (b x^2\right )^{3/2} \, dx &=\frac {\left (b \sqrt {b x^2}\right ) \int x^3 \, dx}{x}\\ &=\frac {1}{4} b x^3 \sqrt {b x^2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 0.82 \[ \frac {1}{4} x \left (b x^2\right )^{3/2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.72, size = 13, normalized size = 0.76 \[ \frac {1}{4} \, \sqrt {b x^{2}} b x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 10, normalized size = 0.59 \[ \frac {1}{4} \, b^{\frac {3}{2}} x^{4} \mathrm {sgn}\relax (x) \]
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 \[ \frac {\left (b \,x^{2}\right )^{\frac {3}{2}} x}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.31, size = 10, normalized size = 0.59 \[ \frac {1}{4} \, \left (b x^{2}\right )^{\frac {3}{2}} x \]
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 \[ \int {\left (b\,x^2\right )}^{3/2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.39, size = 14, normalized size = 0.82 \[ \frac {b^{\frac {3}{2}} x \left (x^{2}\right )^{\frac {3}{2}}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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