Optimal. Leaf size=25 \[ -\frac{x^{7/2}}{7 b \left (a x+b x^3\right )^{7/2}} \]
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Rubi [A] time = 0.0370535, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053, Rules used = {2014} \[ -\frac{x^{7/2}}{7 b \left (a x+b x^3\right )^{7/2}} \]
Antiderivative was successfully verified.
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Rule 2014
Rubi steps
\begin{align*} \int \frac{x^{11/2}}{\left (a x+b x^3\right )^{9/2}} \, dx &=-\frac{x^{7/2}}{7 b \left (a x+b x^3\right )^{7/2}}\\ \end{align*}
Mathematica [A] time = 0.0135167, size = 25, normalized size = 1. \[ -\frac{x^{7/2}}{7 b \left (x \left (a+b x^2\right )\right )^{7/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 27, normalized size = 1.1 \begin{align*} -{\frac{b{x}^{2}+a}{7\,b}{x}^{{\frac{9}{2}}} \left ( b{x}^{3}+ax \right ) ^{-{\frac{9}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x^{\frac{11}{2}}}{{\left (b x^{3} + a x\right )}^{\frac{9}{2}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.70886, size = 132, normalized size = 5.28 \begin{align*} -\frac{\sqrt{b x^{3} + a x} \sqrt{x}}{7 \,{\left (b^{5} x^{9} + 4 \, a b^{4} x^{7} + 6 \, a^{2} b^{3} x^{5} + 4 \, a^{3} b^{2} x^{3} + a^{4} b x\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.27413, size = 31, normalized size = 1.24 \begin{align*} -\frac{1}{7 \,{\left (b x^{2} + a\right )}^{\frac{7}{2}} b} + \frac{1}{7 \, a^{\frac{7}{2}} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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