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 = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {15, 30} \begin {gather*} -\frac {1}{3 x^2 \sqrt {b x^2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {1}{x^3 \sqrt {b x^2}} \, dx &=\frac {x \int \frac {1}{x^4} \, dx}{\sqrt {b x^2}}\\ &=-\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 \begin {gather*} -\frac {1}{3 x^2 \sqrt {b x^2}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 14, normalized size = 0.88 \begin {gather*} -\frac {b}{3 \left (b x^2\right )^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.86, size = 15, normalized size = 0.94 \begin {gather*} -\frac {\sqrt {b x^{2}}}{3 \, b x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 12, normalized size = 0.75 \begin {gather*} -\frac {1}{3 \, \sqrt {b x^{2}} x^{2}} \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 {1}{3 \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 = 1.33, size = 8, normalized size = 0.50 \begin {gather*} -\frac {1}{3 \, \sqrt {b} x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.97, size = 10, normalized size = 0.62 \begin {gather*} -\frac {1}{3\,\sqrt {b}\,{\left (x^2\right )}^{3/2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.62, size = 19, normalized size = 1.19 \begin {gather*} - \frac {1}{3 \sqrt {b} x^{2} \sqrt {x^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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