Optimal. Leaf size=16 \[ \frac {1}{3} x^2 \sqrt {b x^2} \]
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Rubi [A] time = 0.00, antiderivative size = 16, 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} \[ \frac {1}{3} x^2 \sqrt {b x^2} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int x \sqrt {b x^2} \, dx &=\frac {\sqrt {b x^2} \int x^2 \, dx}{x}\\ &=\frac {1}{3} x^2 \sqrt {b x^2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \[ \frac {1}{3} x^2 \sqrt {b x^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 12, normalized size = 0.75 \[ \frac {1}{3} \, \sqrt {b x^{2}} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 10, normalized size = 0.62 \[ \frac {1}{3} \, \sqrt {b} x^{3} \mathrm {sgn}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.81 \[ \frac {\sqrt {b \,x^{2}}\, x^{2}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.31, size = 12, normalized size = 0.75 \[ \frac {\left (b x^{2}\right )^{\frac {3}{2}}}{3 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.02, size = 10, normalized size = 0.62 \[ \frac {\sqrt {b}\,\sqrt {x^6}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 15, normalized size = 0.94 \[ \frac {\sqrt {b} x^{2} \sqrt {x^{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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