Optimal. Leaf size=12 \[ -\frac {2 x}{\sqrt {b x^3}} \]
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Rubi [A] time = 0.00, antiderivative size = 12, 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 {2 x}{\sqrt {b x^3}} \end {gather*}
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {1}{\sqrt {b x^3}} \, dx &=\frac {x^{3/2} \int \frac {1}{x^{3/2}} \, dx}{\sqrt {b x^3}}\\ &=-\frac {2 x}{\sqrt {b x^3}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 1.00 \begin {gather*} -\frac {2 x}{\sqrt {b x^3}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 17, normalized size = 1.42 \begin {gather*} -\frac {2 \sqrt {b x^3}}{b x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.20, size = 15, normalized size = 1.25 \begin {gather*} -\frac {2 \, \sqrt {b x^{3}}}{b x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 11, normalized size = 0.92 \begin {gather*} -\frac {2}{\sqrt {b x} \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 = 0.92 \begin {gather*} -\frac {2 x}{\sqrt {b \,x^{3}}} \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 = 0.83 \begin {gather*} -\frac {2 \, x}{\sqrt {b x^{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.94, size = 15, normalized size = 1.25 \begin {gather*} -\frac {2\,\sqrt {b\,x^3}}{b\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.40, size = 15, normalized size = 1.25 \begin {gather*} - \frac {2 x}{\sqrt {b} \sqrt {x^{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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