Optimal. Leaf size=14 \[ -\frac {1}{b^2 \sqrt {b x^2}} \]
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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 = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {15, 30} \[ -\frac {1}{b^2 \sqrt {b x^2}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {x^3}{\left (b x^2\right )^{5/2}} \, dx &=\frac {x \int \frac {1}{x^2} \, dx}{b^2 \sqrt {b x^2}}\\ &=-\frac {1}{b^2 \sqrt {b x^2}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \[ -\frac {x^4}{\left (b x^2\right )^{5/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 15, normalized size = 1.07 \[ -\frac {\sqrt {b x^{2}}}{b^{3} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 12, normalized size = 0.86 \[ -\frac {1}{\sqrt {b x^{2}} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.93 \[ -\frac {x^{4}}{\left (b \,x^{2}\right )^{\frac {5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.33, size = 15, normalized size = 1.07 \[ -\frac {x^{2}}{\left (b x^{2}\right )^{\frac {3}{2}} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.98, size = 10, normalized size = 0.71 \[ -\frac {1}{b^{5/2}\,\sqrt {x^2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.86, size = 15, normalized size = 1.07 \[ - \frac {x^{4}}{b^{\frac {5}{2}} \left (x^{2}\right )^{\frac {5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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