Optimal. Leaf size=15 \[ \frac{5}{2} \sqrt{x^{4/5}+1} \]
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Rubi [A] time = 0.0030842, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059, Rules used = {261} \[ \frac{5}{2} \sqrt{x^{4/5}+1} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{1}{\sqrt{1+x^{4/5}} \sqrt [5]{x}} \, dx &=\frac{5}{2} \sqrt{1+x^{4/5}}\\ \end{align*}
Mathematica [A] time = 0.00373, size = 15, normalized size = 1. \[ \frac{5}{2} \sqrt{x^{4/5}+1} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 10, normalized size = 0.7 \begin{align*}{\frac{5}{2}\sqrt{1+{x}^{{\frac{4}{5}}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00518, size = 12, normalized size = 0.8 \begin{align*} \frac{5}{2} \, \sqrt{x^{\frac{4}{5}} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.857914, size = 12, normalized size = 0.8 \begin{align*} \frac{5 \sqrt{x^{\frac{4}{5}} + 1}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1832, size = 12, normalized size = 0.8 \begin{align*} \frac{5}{2} \, \sqrt{x^{\frac{4}{5}} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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