Optimal. Leaf size=14 \[ \frac {1}{2} x \sqrt {b x^2} \]
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Rubi [A] time = 0.00, antiderivative size = 14, 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} \begin {gather*} \frac {1}{2} x \sqrt {b x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \sqrt {b x^2} \, dx &=\frac {\sqrt {b x^2} \int x \, dx}{x}\\ &=\frac {1}{2} x \sqrt {b x^2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} \frac {1}{2} x \sqrt {b x^2} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} \frac {1}{2} x \sqrt {b x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.92, size = 10, normalized size = 0.71 \begin {gather*} \frac {1}{2} \, \sqrt {b x^{2}} x \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 = 0.71 \begin {gather*} \frac {1}{2} \, \sqrt {b} x^{2} \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 = 11, normalized size = 0.79 \begin {gather*} \frac {\sqrt {b \,x^{2}}\, x}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.32, size = 10, normalized size = 0.71 \begin {gather*} \frac {1}{2} \, \sqrt {b x^{2}} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.00, size = 8, normalized size = 0.57 \begin {gather*} \frac {\sqrt {b}\,x\,\relax |x|}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 14, normalized size = 1.00 \begin {gather*} \frac {\sqrt {b} x \sqrt {x^{2}}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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