Optimal. Leaf size=19 \[ \frac {x^4}{3 b \sqrt {b x^2}} \]
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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} \[ \frac {x^4}{3 b \sqrt {b x^2}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {x^5}{\left (b x^2\right )^{3/2}} \, dx &=\frac {x \int x^2 \, dx}{b \sqrt {b x^2}}\\ &=\frac {x^4}{3 b \sqrt {b x^2}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 0.84 \[ \frac {x^6}{3 \left (b x^2\right )^{3/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.70, size = 15, normalized size = 0.79 \[ \frac {\sqrt {b x^{2}} x^{2}}{3 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 15, normalized size = 0.79 \[ \frac {\sqrt {b x^{2}} x^{2}}{3 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.68 \[ \frac {x^{6}}{3 \left (b \,x^{2}\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.30, size = 15, normalized size = 0.79 \[ \frac {x^{4}}{3 \, \sqrt {b x^{2}} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.02, size = 10, normalized size = 0.53 \[ \frac {\sqrt {x^6}}{3\,b^{3/2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.71, size = 15, normalized size = 0.79 \[ \frac {x^{6}}{3 b^{\frac {3}{2}} \left (x^{2}\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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