Optimal. Leaf size=18 \[ -\frac {2 \left (a+\frac {b}{x^3}\right )^{5/2}}{15 b} \]
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Rubi [A] time = 0.01, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {261} \[ -\frac {2 \left (a+\frac {b}{x^3}\right )^{5/2}}{15 b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int \frac {\left (a+\frac {b}{x^3}\right )^{3/2}}{x^4} \, dx &=-\frac {2 \left (a+\frac {b}{x^3}\right )^{5/2}}{15 b}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 28, normalized size = 1.56 \[ -\frac {2 \left (a+\frac {b}{x^3}\right )^{3/2} \left (a x^3+b\right )}{15 b x^3} \]
Antiderivative was successfully verified.
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fricas [B] time = 1.05, size = 39, normalized size = 2.17 \[ -\frac {2 \, {\left (a^{2} x^{6} + 2 \, a b x^{3} + b^{2}\right )} \sqrt {\frac {a x^{3} + b}{x^{3}}}}{15 \, b x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 14, normalized size = 0.78 \[ -\frac {2 \, {\left (a + \frac {b}{x^{3}}\right )}^{\frac {5}{2}}}{15 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 29, normalized size = 1.61 \[ -\frac {2 \left (a \,x^{3}+b \right ) \left (\frac {a \,x^{3}+b}{x^{3}}\right )^{\frac {3}{2}}}{15 b \,x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.85, size = 14, normalized size = 0.78 \[ -\frac {2 \, {\left (a + \frac {b}{x^{3}}\right )}^{\frac {5}{2}}}{15 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.89, size = 26, normalized size = 1.44 \[ -\frac {2\,\sqrt {a+\frac {b}{x^3}}\,{\left (a\,x^3+b\right )}^2}{15\,b\,x^6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.36, size = 71, normalized size = 3.94 \[ - \frac {2 a^{\frac {5}{2}} \sqrt {1 + \frac {b}{a x^{3}}}}{15 b} - \frac {4 a^{\frac {3}{2}} \sqrt {1 + \frac {b}{a x^{3}}}}{15 x^{3}} - \frac {2 \sqrt {a} b \sqrt {1 + \frac {b}{a x^{3}}}}{15 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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