Optimal. Leaf size=17 \[ \frac {1}{5} b x^4 \sqrt {b x^2} \]
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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 = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {15, 30} \[ \frac {1}{5} b x^4 \sqrt {b x^2} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int x \left (b x^2\right )^{3/2} \, dx &=\frac {\left (b \sqrt {b x^2}\right ) \int x^4 \, dx}{x}\\ &=\frac {1}{5} b x^4 \sqrt {b x^2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 0.94 \[ \frac {1}{5} x^2 \left (b x^2\right )^{3/2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.75, size = 13, normalized size = 0.76 \[ \frac {1}{5} \, \sqrt {b x^{2}} b x^{4} \]
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 \[ \frac {1}{5} \, b^{\frac {3}{2}} x^{5} \mathrm {sgn}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.76 \[ \frac {\left (b \,x^{2}\right )^{\frac {3}{2}} x^{2}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.33, size = 12, normalized size = 0.71 \[ \frac {\left (b x^{2}\right )^{\frac {5}{2}}}{5 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.96, size = 10, normalized size = 0.59 \[ \frac {b^{3/2}\,\sqrt {x^{10}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.51, size = 15, normalized size = 0.88 \[ \frac {b^{\frac {3}{2}} x^{2} \left (x^{2}\right )^{\frac {3}{2}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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