Optimal. Leaf size=11 \[ b \sqrt {b x^2} \]
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Rubi [A]
time = 0.00, antiderivative size = 11, 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}
\begin {gather*} b \sqrt {b x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 8
Rule 15
Rubi steps
\begin {align*} \int \frac {\left (b x^2\right )^{3/2}}{x^3} \, dx &=\frac {\left (b \sqrt {b x^2}\right ) \int 1 \, dx}{x}\\ &=b \sqrt {b x^2}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 13, normalized size = 1.18 \begin {gather*} \frac {\left (b x^2\right )^{3/2}}{x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 12, normalized size = 1.09
method | result | size |
risch | \(b \sqrt {b \,x^{2}}\) | \(10\) |
default | \(\frac {\left (b \,x^{2}\right )^{\frac {3}{2}}}{x^{2}}\) | \(12\) |
trager | \(\frac {b \left (x -1\right ) \sqrt {b \,x^{2}}}{x}\) | \(16\) |
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 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 9, normalized size = 0.82 \begin {gather*} \sqrt {b x^{2}} b \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.18, size = 10, normalized size = 0.91 \begin {gather*} \frac {\left (b x^{2}\right )^{\frac {3}{2}}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.35, size = 7, normalized size = 0.64 \begin {gather*} b^{\frac {3}{2}} x \mathrm {sgn}\left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.90, size = 6, normalized size = 0.55 \begin {gather*} b^{3/2}\,\left |x\right | \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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