Optimal. Leaf size=15 \[ \frac{\sqrt [4]{a+b x^4}}{b} \]
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Rubi [A] time = 0.0041534, antiderivative size = 15, 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 = {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 = 0.0032187, size = 15, normalized size = 1. \[ \frac{\sqrt [4]{a+b x^4}}{b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 14, 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 = 0.980361, size = 18, normalized size = 1.2 \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 = 1.45121, size = 28, normalized size = 1.87 \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 = 0.605711, size = 20, normalized size = 1.33 \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 = 1.12206, size = 18, normalized size = 1.2 \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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