Optimal. Leaf size=9 \[ \sqrt {b x^2} \]
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Rubi [A] time = 0.00, antiderivative size = 9, 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} \[ \sqrt {b x^2} \]
Antiderivative was successfully verified.
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Rule 8
Rule 15
Rubi steps
\begin {align*} \int \frac {\sqrt {b x^2}}{x} \, dx &=\frac {\sqrt {b x^2} \int 1 \, dx}{x}\\ &=\sqrt {b x^2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 1.56 \[ \frac {b x^2}{\sqrt {b x^2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.72, size = 7, normalized size = 0.78 \[ \sqrt {b x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 7, normalized size = 0.78 \[ \sqrt {b} x \mathrm {sgn}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 8, normalized size = 0.89 \[ \sqrt {b \,x^{2}} \]
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 = 0.93, size = 6, normalized size = 0.67 \[ \sqrt {b}\,\relax |x| \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 10, normalized size = 1.11 \[ \sqrt {b} \sqrt {x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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