Optimal. Leaf size=16 \[ \frac {1}{5} x^4 \sqrt {b x^2} \]
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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 = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {15, 30} \begin {gather*} \frac {1}{5} x^4 \sqrt {b x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int x^3 \sqrt {b x^2} \, dx &=\frac {\sqrt {b x^2} \int x^4 \, dx}{x}\\ &=\frac {1}{5} x^4 \sqrt {b x^2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \begin {gather*} \frac {1}{5} x^4 \sqrt {b x^2} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 16, normalized size = 1.00 \begin {gather*} \frac {\left (b x^2\right )^{5/2}}{5 b^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.78, size = 12, normalized size = 0.75 \begin {gather*} \frac {1}{5} \, \sqrt {b x^{2}} x^{4} \end {gather*}
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 \begin {gather*} \frac {1}{5} \, \sqrt {b} x^{5} \mathrm {sgn}\relax (x) \end {gather*}
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 \begin {gather*} \frac {\sqrt {b \,x^{2}}\, x^{4}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.29, size = 15, normalized size = 0.94 \begin {gather*} \frac {\left (b x^{2}\right )^{\frac {3}{2}} x^{2}}{5 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.03, size = 10, normalized size = 0.62 \begin {gather*} \frac {\sqrt {b}\,\sqrt {x^{10}}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.30, size = 15, normalized size = 0.94 \begin {gather*} \frac {\sqrt {b} x^{4} \sqrt {x^{2}}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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