Optimal. Leaf size=15 \[ \frac {2}{3} \left (x^5+2 x\right )^{3/2} \]
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Rubi [A] time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.03, size = 15, normalized size = 1.00 \[ \frac {2}{3} \left (x \left (x^4+2\right )\right )^{3/2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 11, normalized size = 0.73 \[ \frac {2}{3} \, {\left (x^{5} + 2 \, x\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.40, size = 11, normalized size = 0.73 \[ \frac {2}{3} \, {\left (x^{5} + 2 \, x\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 18, normalized size = 1.20 \[ \frac {2 \left (x^{4}+2\right ) \sqrt {x^{5}+2 x}\, x}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.87, size = 11, normalized size = 0.73 \[ \frac {2}{3} \, {\left (x^{5} + 2 \, x\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.11, size = 11, normalized size = 0.73 \[ \frac {2\,{\left (x^5+2\,x\right )}^{3/2}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.26, size = 31, normalized size = 2.07 \[ \frac {2 x^{5} \sqrt {x^{5} + 2 x}}{3} + \frac {4 x \sqrt {x^{5} + 2 x}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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