Optimal. Leaf size=19 \[ -\frac{\left (a-b x^4\right )^{3/4}}{3 b} \]
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Rubi [A] time = 0.0041099, 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} \[ -\frac{\left (a-b x^4\right )^{3/4}}{3 b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{x^3}{\sqrt [4]{a-b x^4}} \, dx &=-\frac{\left (a-b x^4\right )^{3/4}}{3 b}\\ \end{align*}
Mathematica [A] time = 0.0038246, size = 19, normalized size = 1. \[ -\frac{\left (a-b x^4\right )^{3/4}}{3 b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 16, normalized size = 0.8 \begin{align*} -{\frac{1}{3\,b} \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 = 0.98267, size = 20, normalized size = 1.05 \begin{align*} -\frac{{\left (-b x^{4} + a\right )}^{\frac{3}{4}}}{3 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.4713, size = 36, normalized size = 1.89 \begin{align*} -\frac{{\left (-b x^{4} + a\right )}^{\frac{3}{4}}}{3 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.601348, size = 24, normalized size = 1.26 \begin{align*} \begin{cases} - \frac{\left (a - b x^{4}\right )^{\frac{3}{4}}}{3 b} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 \sqrt [4]{a}} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12089, size = 20, normalized size = 1.05 \begin{align*} -\frac{{\left (-b x^{4} + a\right )}^{\frac{3}{4}}}{3 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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