Optimal. Leaf size=17 \[ -\frac {b \sqrt {b x^2}}{2 x^3} \]
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Rubi [A] time = 0.00, antiderivative size = 17, 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} \[ -\frac {b \sqrt {b x^2}}{2 x^3} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {\left (b x^2\right )^{3/2}}{x^6} \, dx &=\frac {\left (b \sqrt {b x^2}\right ) \int \frac {1}{x^3} \, dx}{x}\\ &=-\frac {b \sqrt {b x^2}}{2 x^3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 0.94 \[ -\frac {\left (b x^2\right )^{3/2}}{2 x^5} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.48, size = 13, normalized size = 0.76 \[ -\frac {\sqrt {b x^{2}} b}{2 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 10, normalized size = 0.59 \[ -\frac {b^{\frac {3}{2}} \mathrm {sgn}\relax (x)}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.76 \[ -\frac {\left (b \,x^{2}\right )^{\frac {3}{2}}}{2 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: RuntimeError} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.90, size = 13, normalized size = 0.76 \[ -\frac {b^{3/2}}{2\,x\,\sqrt {x^2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.02, size = 17, normalized size = 1.00 \[ - \frac {b^{\frac {3}{2}} \left (x^{2}\right )^{\frac {3}{2}}}{2 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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