Optimal. Leaf size=22 \[ -\frac{\left (a-b x^4\right )^{3/4}}{3 a x^3} \]
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Rubi [A] time = 0.0046507, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062, Rules used = {264} \[ -\frac{\left (a-b x^4\right )^{3/4}}{3 a x^3} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{1}{x^4 \sqrt [4]{a-b x^4}} \, dx &=-\frac{\left (a-b x^4\right )^{3/4}}{3 a x^3}\\ \end{align*}
Mathematica [A] time = 0.0041998, size = 22, normalized size = 1. \[ -\frac{\left (a-b x^4\right )^{3/4}}{3 a x^3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 19, normalized size = 0.9 \begin{align*} -{\frac{1}{3\,a{x}^{3}} \left ( -b{x}^{4}+a \right ) ^{{\frac{3}{4}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.982862, size = 24, normalized size = 1.09 \begin{align*} -\frac{{\left (-b x^{4} + a\right )}^{\frac{3}{4}}}{3 \, a x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.78086, size = 45, normalized size = 2.05 \begin{align*} -\frac{{\left (-b x^{4} + a\right )}^{\frac{3}{4}}}{3 \, a x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.00889, size = 82, normalized size = 3.73 \begin{align*} \begin{cases} \frac{b^{\frac{3}{4}} \left (\frac{a}{b x^{4}} - 1\right )^{\frac{3}{4}} \Gamma \left (- \frac{3}{4}\right )}{4 a \Gamma \left (\frac{1}{4}\right )} & \text{for}\: \frac{\left |{a}\right |}{\left |{b}\right | \left |{x^{4}}\right |} > 1 \\- \frac{b^{\frac{3}{4}} \left (- \frac{a}{b x^{4}} + 1\right )^{\frac{3}{4}} e^{- \frac{i \pi }{4}} \Gamma \left (- \frac{3}{4}\right )}{4 a \Gamma \left (\frac{1}{4}\right )} & \text{otherwise} \end{cases} \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{1}{4}} x^{4}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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