Optimal. Leaf size=16 \[ \frac {x^2}{b^2 \sqrt {b x^2}} \]
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Rubi [A] time = 0.00, antiderivative size = 16, 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, 8} \[ \frac {x^2}{b^2 \sqrt {b x^2}} \]
Antiderivative was successfully verified.
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Rule 8
Rule 15
Rubi steps
\begin {align*} \int \frac {x^5}{\left (b x^2\right )^{5/2}} \, dx &=\frac {x \int 1 \, dx}{b^2 \sqrt {b x^2}}\\ &=\frac {x^2}{b^2 \sqrt {b x^2}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 0.81 \[ \frac {x^6}{\left (b x^2\right )^{5/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 11, normalized size = 0.69 \[ \frac {\sqrt {b x^{2}}}{b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 11, normalized size = 0.69 \[ \frac {\sqrt {b x^{2}}}{b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 12, normalized size = 0.75 \[ \frac {x^{6}}{\left (b \,x^{2}\right )^{\frac {5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.29, size = 14, normalized size = 0.88 \[ \frac {x^{4}}{\left (b x^{2}\right )^{\frac {3}{2}} b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.96, size = 6, normalized size = 0.38 \[ \frac {\relax |x|}{b^{5/2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.83, size = 14, normalized size = 0.88 \[ \frac {x^{6}}{b^{\frac {5}{2}} \left (x^{2}\right )^{\frac {5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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