Optimal. Leaf size=19 \[ \frac {2 x^4}{11 b \sqrt {\frac {b}{x^3}}} \]
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Rubi [A]
time = 0.00, antiderivative size = 19, 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*} \frac {2 x^4}{11 b \sqrt {\frac {b}{x^3}}} \end {gather*}
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {1}{\left (\frac {b}{x^3}\right )^{3/2}} \, dx &=\frac {\int x^{9/2} \, dx}{b \sqrt {\frac {b}{x^3}} x^{3/2}}\\ &=\frac {2 x^4}{11 b \sqrt {\frac {b}{x^3}}}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 14, normalized size = 0.74 \begin {gather*} \frac {2 x}{11 \left (\frac {b}{x^3}\right )^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 11, normalized size = 0.58
method | result | size |
gosper | \(\frac {2 x}{11 \left (\frac {b}{x^{3}}\right )^{\frac {3}{2}}}\) | \(11\) |
default | \(\frac {2 x}{11 \left (\frac {b}{x^{3}}\right )^{\frac {3}{2}}}\) | \(11\) |
trager | \(\frac {2 x^{7} \sqrt {\frac {b}{x^{3}}}}{11 b^{2}}\) | \(16\) |
risch | \(\frac {2 x^{4}}{11 b \sqrt {\frac {b}{x^{3}}}}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 10, normalized size = 0.53 \begin {gather*} \frac {2 \, x}{11 \, \left (\frac {b}{x^{3}}\right )^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 15, normalized size = 0.79 \begin {gather*} \frac {2 \, x^{7} \sqrt {\frac {b}{x^{3}}}}{11 \, b^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.19, size = 12, normalized size = 0.63 \begin {gather*} \frac {2 x}{11 \left (\frac {b}{x^{3}}\right )^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.53, size = 13, normalized size = 0.68 \begin {gather*} \frac {2 \, \sqrt {b x} x^{5}}{11 \, b^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.95, size = 15, normalized size = 0.79 \begin {gather*} \frac {2\,x^7\,\sqrt {\frac {b}{x^3}}}{11\,b^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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