Optimal. Leaf size=21 \[ -\frac{\left (a+c x^4\right )^{5/2}}{10 a x^{10}} \]
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Rubi [A] time = 0.0047694, antiderivative size = 21, normalized size of antiderivative = 1., 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 = {264} \[ -\frac{\left (a+c x^4\right )^{5/2}}{10 a x^{10}} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{\left (a+c x^4\right )^{3/2}}{x^{11}} \, dx &=-\frac{\left (a+c x^4\right )^{5/2}}{10 a x^{10}}\\ \end{align*}
Mathematica [A] time = 0.0053433, size = 21, normalized size = 1. \[ -\frac{\left (a+c x^4\right )^{5/2}}{10 a x^{10}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 18, normalized size = 0.9 \begin{align*} -{\frac{1}{10\,a{x}^{10}} \left ( c{x}^{4}+a \right ) ^{{\frac{5}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.959087, size = 23, normalized size = 1.1 \begin{align*} -\frac{{\left (c x^{4} + a\right )}^{\frac{5}{2}}}{10 \, a x^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.48456, size = 81, normalized size = 3.86 \begin{align*} -\frac{{\left (c^{2} x^{8} + 2 \, a c x^{4} + a^{2}\right )} \sqrt{c x^{4} + a}}{10 \, a x^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 2.63643, size = 66, normalized size = 3.14 \begin{align*} - \frac{a \sqrt{c} \sqrt{\frac{a}{c x^{4}} + 1}}{10 x^{8}} - \frac{c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{4}} + 1}}{5 x^{4}} - \frac{c^{\frac{5}{2}} \sqrt{\frac{a}{c x^{4}} + 1}}{10 a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1187, size = 19, normalized size = 0.9 \begin{align*} -\frac{{\left (c + \frac{a}{x^{4}}\right )}^{\frac{5}{2}}}{10 \, a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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