Optimal. Leaf size=18 \[ \frac{\left (a+b x^4\right )^{5/4}}{5 b} \]
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Rubi [A] time = 0.0038969, 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} \[ \frac{\left (a+b x^4\right )^{5/4}}{5 b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int x^3 \sqrt [4]{a+b x^4} \, dx &=\frac{\left (a+b x^4\right )^{5/4}}{5 b}\\ \end{align*}
Mathematica [A] time = 0.0031529, size = 18, normalized size = 1. \[ \frac{\left (a+b x^4\right )^{5/4}}{5 b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 15, normalized size = 0.8 \begin{align*}{\frac{1}{5\,b} \left ( b{x}^{4}+a \right ) ^{{\frac{5}{4}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.955124, size = 19, normalized size = 1.06 \begin{align*} \frac{{\left (b x^{4} + a\right )}^{\frac{5}{4}}}{5 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.42235, size = 34, normalized size = 1.89 \begin{align*} \frac{{\left (b x^{4} + a\right )}^{\frac{5}{4}}}{5 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.641596, size = 39, normalized size = 2.17 \begin{align*} \begin{cases} \frac{a \sqrt [4]{a + b x^{4}}}{5 b} + \frac{x^{4} \sqrt [4]{a + b x^{4}}}{5} & \text{for}\: b \neq 0 \\\frac{\sqrt [4]{a} x^{4}}{4} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15703, size = 19, normalized size = 1.06 \begin{align*} \frac{{\left (b x^{4} + a\right )}^{\frac{5}{4}}}{5 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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