Optimal. Leaf size=19 \[ -\frac{\sqrt{a-b x^4}}{2 b} \]
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Rubi [A] time = 0.0043524, antiderivative size = 19, 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} \[ -\frac{\sqrt{a-b x^4}}{2 b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{x^3}{\sqrt{a-b x^4}} \, dx &=-\frac{\sqrt{a-b x^4}}{2 b}\\ \end{align*}
Mathematica [A] time = 0.0042814, size = 19, normalized size = 1. \[ -\frac{\sqrt{a-b x^4}}{2 b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 16, normalized size = 0.8 \begin{align*} -{\frac{1}{2\,b}\sqrt{-b{x}^{4}+a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.972779, size = 20, normalized size = 1.05 \begin{align*} -\frac{\sqrt{-b x^{4} + a}}{2 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.44779, size = 34, normalized size = 1.79 \begin{align*} -\frac{\sqrt{-b x^{4} + a}}{2 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.609188, size = 24, normalized size = 1.26 \begin{align*} \begin{cases} - \frac{\sqrt{a - b x^{4}}}{2 b} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 \sqrt{a}} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11519, size = 20, normalized size = 1.05 \begin{align*} -\frac{\sqrt{-b x^{4} + a}}{2 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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