Optimal. Leaf size=13 \[ b^2 \sqrt {b x^2} \]
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Rubi [A] time = 0.00, antiderivative size = 13, 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} \[ b^2 \sqrt {b x^2} \]
Antiderivative was successfully verified.
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Rule 8
Rule 15
Rubi steps
\begin {align*} \int \frac {\left (b x^2\right )^{5/2}}{x^5} \, dx &=\frac {\left (b^2 \sqrt {b x^2}\right ) \int 1 \, dx}{x}\\ &=b^2 \sqrt {b x^2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 1.00 \[ \frac {\left (b x^2\right )^{5/2}}{x^4} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.52, size = 11, normalized size = 0.85 \[ \sqrt {b x^{2}} b^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 7, normalized size = 0.54 \[ b^{\frac {5}{2}} x \mathrm {sgn}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 12, normalized size = 0.92 \[ \frac {\left (b \,x^{2}\right )^{\frac {5}{2}}}{x^{4}} \]
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 = 0.95, size = 6, normalized size = 0.46 \[ b^{5/2}\,\relax |x| \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.24, size = 14, normalized size = 1.08 \[ \frac {b^{\frac {5}{2}} \left (x^{2}\right )^{\frac {5}{2}}}{x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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