Optimal. Leaf size=18 \[ \frac{\sqrt{a+b x^4}}{2 b} \]
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Rubi [A] time = 0.0044366, antiderivative size = 18, 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} \[ \frac{\sqrt{a+b x^4}}{2 b} \]
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 = 0.0028254, size = 18, normalized size = 1. \[ \frac{\sqrt{a+b x^4}}{2 b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 15, 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 = 0.966064, size = 19, normalized size = 1.06 \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 = 1.46437, size = 31, normalized size = 1.72 \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 = 0.650496, size = 22, normalized size = 1.22 \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 = 1.1088, size = 19, normalized size = 1.06 \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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