Optimal. Leaf size=16 \[ -\frac{1}{b \sqrt [4]{a+b x^4}} \]
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Rubi [A] time = 0.0044063, antiderivative size = 16, 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} \[ -\frac{1}{b \sqrt [4]{a+b x^4}} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{x^3}{\left (a+b x^4\right )^{5/4}} \, dx &=-\frac{1}{b \sqrt [4]{a+b x^4}}\\ \end{align*}
Mathematica [A] time = 0.0037204, size = 16, normalized size = 1. \[ -\frac{1}{b \sqrt [4]{a+b x^4}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 15, normalized size = 0.9 \begin{align*} -{\frac{1}{b}{\frac{1}{\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 = 0.967929, size = 19, normalized size = 1.19 \begin{align*} -\frac{1}{{\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 = 1.46153, size = 49, normalized size = 3.06 \begin{align*} -\frac{{\left (b x^{4} + a\right )}^{\frac{3}{4}}}{b^{2} x^{4} + a b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.72364, size = 24, normalized size = 1.5 \begin{align*} \begin{cases} - \frac{1}{b \sqrt [4]{a + b x^{4}}} & \text{for}\: b \neq 0 \\\frac{x^{4}}{4 a^{\frac{5}{4}}} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09973, size = 19, normalized size = 1.19 \begin{align*} -\frac{1}{{\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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