Optimal. Leaf size=15 \[ \frac{2}{3} \left (x^5+2 x\right )^{3/2} \]
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Rubi [A] time = 0.0083743, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053, Rules used = {1588} \[ \frac{2}{3} \left (x^5+2 x\right )^{3/2} \]
Antiderivative was successfully verified.
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Rule 1588
Rubi steps
\begin{align*} \int \left (2+5 x^4\right ) \sqrt{2 x+x^5} \, dx &=\frac{2}{3} \left (2 x+x^5\right )^{3/2}\\ \end{align*}
Mathematica [A] time = 0.0339676, size = 15, normalized size = 1. \[ \frac{2}{3} \left (x \left (x^4+2\right )\right )^{3/2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 18, normalized size = 1.2 \begin{align*}{\frac{2\,x \left ({x}^{4}+2 \right ) }{3}\sqrt{{x}^{5}+2\,x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.08896, size = 15, normalized size = 1. \begin{align*} \frac{2}{3} \,{\left (x^{5} + 2 \, x\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.44811, size = 31, normalized size = 2.07 \begin{align*} \frac{2}{3} \,{\left (x^{5} + 2 \, x\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.243079, size = 31, normalized size = 2.07 \begin{align*} \frac{2 x^{5} \sqrt{x^{5} + 2 x}}{3} + \frac{4 x \sqrt{x^{5} + 2 x}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14557, size = 15, normalized size = 1. \begin{align*} \frac{2}{3} \,{\left (x^{5} + 2 \, x\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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