Optimal. Leaf size=21 \[ -\frac{\left (a+b x^4\right )^{9/4}}{9 a x^9} \]
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Rubi [A] time = 0.0045641, 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} \[ -\frac{\left (a+b x^4\right )^{9/4}}{9 a x^9} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{\left (a+b x^4\right )^{5/4}}{x^{10}} \, dx &=-\frac{\left (a+b x^4\right )^{9/4}}{9 a x^9}\\ \end{align*}
Mathematica [A] time = 0.0057183, size = 21, normalized size = 1. \[ -\frac{\left (a+b x^4\right )^{9/4}}{9 a x^9} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 18, normalized size = 0.9 \begin{align*} -{\frac{1}{9\,a{x}^{9}} \left ( b{x}^{4}+a \right ) ^{{\frac{9}{4}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.97999, size = 23, normalized size = 1.1 \begin{align*} -\frac{{\left (b x^{4} + a\right )}^{\frac{9}{4}}}{9 \, a x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 2.03512, size = 81, normalized size = 3.86 \begin{align*} -\frac{{\left (b^{2} x^{8} + 2 \, a b x^{4} + a^{2}\right )}{\left (b x^{4} + a\right )}^{\frac{1}{4}}}{9 \, a x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 4.51322, size = 105, normalized size = 5. \begin{align*} \frac{a \sqrt [4]{b} \sqrt [4]{\frac{a}{b x^{4}} + 1} \Gamma \left (- \frac{9}{4}\right )}{4 x^{8} \Gamma \left (- \frac{5}{4}\right )} + \frac{b^{\frac{5}{4}} \sqrt [4]{\frac{a}{b x^{4}} + 1} \Gamma \left (- \frac{9}{4}\right )}{2 x^{4} \Gamma \left (- \frac{5}{4}\right )} + \frac{b^{\frac{9}{4}} \sqrt [4]{\frac{a}{b x^{4}} + 1} \Gamma \left (- \frac{9}{4}\right )}{4 a \Gamma \left (- \frac{5}{4}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.13721, size = 47, normalized size = 2.24 \begin{align*} -\frac{{\left (b^{2} x^{8} + 2 \, a b x^{4} + a^{2}\right )}{\left (b x^{4} + a\right )}^{\frac{1}{4}}}{9 \, a x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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