Optimal. Leaf size=12 \[ -2 b \sqrt {\frac {b}{x}} \]
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Rubi [A]
time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {15, 30}
\begin {gather*} -2 b \sqrt {\frac {b}{x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \left (\frac {b}{x}\right )^{3/2} \, dx &=\left (b \sqrt {\frac {b}{x}} \sqrt {x}\right ) \int \frac {1}{x^{3/2}} \, dx\\ &=-2 b \sqrt {\frac {b}{x}}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 12, normalized size = 1.00 \begin {gather*} -2 \left (\frac {b}{x}\right )^{3/2} x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 11, normalized size = 0.92
method | result | size |
gosper | \(-2 x \left (\frac {b}{x}\right )^{\frac {3}{2}}\) | \(11\) |
default | \(-2 x \left (\frac {b}{x}\right )^{\frac {3}{2}}\) | \(11\) |
trager | \(-2 b \sqrt {\frac {b}{x}}\) | \(11\) |
risch | \(-2 b \sqrt {\frac {b}{x}}\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 10, normalized size = 0.83 \begin {gather*} -2 \, x \left (\frac {b}{x}\right )^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 10, normalized size = 0.83 \begin {gather*} -2 \, b \sqrt {\frac {b}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.11, size = 10, normalized size = 0.83 \begin {gather*} - 2 x \left (\frac {b}{x}\right )^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.84, size = 12, normalized size = 1.00 \begin {gather*} -\frac {2 \, b^{2} \mathrm {sgn}\left (x\right )}{\sqrt {b x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.93, size = 10, normalized size = 0.83 \begin {gather*} -2\,b\,\sqrt {\frac {b}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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