Optimal. Leaf size=17 \[ -\frac{\sqrt [4]{a-b x^4}}{b} \]
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Rubi [A] time = 0.0043918, antiderivative size = 17, 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 = {261} \[ -\frac{\sqrt [4]{a-b x^4}}{b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{x^3}{\left (a-b x^4\right )^{3/4}} \, dx &=-\frac{\sqrt [4]{a-b x^4}}{b}\\ \end{align*}
Mathematica [A] time = 0.0036578, size = 17, normalized size = 1. \[ -\frac{\sqrt [4]{a-b x^4}}{b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 16, normalized size = 0.9 \begin{align*} -{\frac{1}{b}\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 = 1.06784, size = 20, normalized size = 1.18 \begin{align*} -\frac{{\left (-b x^{4} + a\right )}^{\frac{1}{4}}}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.66381, size = 31, normalized size = 1.82 \begin{align*} -\frac{{\left (-b x^{4} + a\right )}^{\frac{1}{4}}}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.607848, size = 22, normalized size = 1.29 \begin{align*} \begin{cases} - \frac{\sqrt [4]{a - b x^{4}}}{b} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{\frac{3}{4}}} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16633, size = 20, normalized size = 1.18 \begin{align*} -\frac{{\left (-b x^{4} + a\right )}^{\frac{1}{4}}}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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