Optimal. Leaf size=19 \[ -\frac{\sqrt [4]{a+b x^4}}{a x} \]
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Rubi [A] time = 0.0063483, antiderivative size = 19, 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} \[ -\frac{\sqrt [4]{a+b x^4}}{a x} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{1}{x^2 \left (a+b x^4\right )^{3/4}} \, dx &=-\frac{\sqrt [4]{a+b x^4}}{a x}\\ \end{align*}
Mathematica [A] time = 0.0037101, size = 19, normalized size = 1. \[ -\frac{\sqrt [4]{a+b x^4}}{a x} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 18, normalized size = 1. \begin{align*} -{\frac{1}{ax}\sqrt [4]{b{x}^{4}+a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0064, size = 23, normalized size = 1.21 \begin{align*} -\frac{{\left (b x^{4} + a\right )}^{\frac{1}{4}}}{a x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.49837, size = 35, normalized size = 1.84 \begin{align*} -\frac{{\left (b x^{4} + a\right )}^{\frac{1}{4}}}{a x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.898897, size = 31, normalized size = 1.63 \begin{align*} \frac{\sqrt [4]{b} \sqrt [4]{\frac{a}{b x^{4}} + 1} \Gamma \left (- \frac{1}{4}\right )}{4 a \Gamma \left (\frac{3}{4}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (b x^{4} + a\right )}^{\frac{3}{4}} x^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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