Optimal. Leaf size=19 \[ -\frac {1}{3 b x^2 \sqrt {b x^2}} \]
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Rubi [A] time = 0.00, antiderivative size = 19, 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 b 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 \left (b x^2\right )^{3/2}} \, dx &=\frac {x \int \frac {1}{x^4} \, dx}{b \sqrt {b x^2}}\\ &=-\frac {1}{3 b x^2 \sqrt {b x^2}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 0.89 \begin {gather*} -\frac {b x^2}{3 \left (b x^2\right )^{5/2}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 13, normalized size = 0.68 \begin {gather*} -\frac {1}{3 \left (b x^2\right )^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.56, size = 15, normalized size = 0.79 \begin {gather*} -\frac {\sqrt {b x^{2}}}{3 \, b^{2} x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 15, normalized size = 0.79 \begin {gather*} -\frac {1}{3 \, \sqrt {b x^{2}} b x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 10, normalized size = 0.53 \begin {gather*} -\frac {1}{3 \left (b \,x^{2}\right )^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.27, size = 8, normalized size = 0.42 \begin {gather*} -\frac {1}{3 \, b^{\frac {3}{2}} x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.96, size = 10, normalized size = 0.53 \begin {gather*} -\frac {1}{3\,b^{3/2}\,{\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 = 0.59, size = 15, normalized size = 0.79 \begin {gather*} - \frac {1}{3 b^{\frac {3}{2}} \left (x^{2}\right )^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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