Optimal. Leaf size=19 \[ -\frac {1}{4 b x^3 \sqrt {b x^2}} \]
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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} \[ -\frac {1}{4 b x^3 \sqrt {b x^2}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {1}{x^2 \left (b x^2\right )^{3/2}} \, dx &=\frac {x \int \frac {1}{x^5} \, dx}{b \sqrt {b x^2}}\\ &=-\frac {1}{4 b x^3 \sqrt {b x^2}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 0.79 \[ -\frac {b x}{4 \left (b x^2\right )^{5/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 15, normalized size = 0.79 \[ -\frac {\sqrt {b x^{2}}}{4 \, b^{2} x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \mathit {sage}_{0} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.68 \[ -\frac {1}{4 \left (b \,x^{2}\right )^{\frac {3}{2}} x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.29, size = 8, normalized size = 0.42 \[ -\frac {1}{4 \, b^{\frac {3}{2}} x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.93, size = 13, normalized size = 0.68 \[ -\frac {1}{4\,b^{3/2}\,x\,{\left (x^2\right )}^{3/2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.73, size = 17, normalized size = 0.89 \[ - \frac {1}{4 b^{\frac {3}{2}} x \left (x^{2}\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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