Optimal. Leaf size=27 \[ \frac {2}{9} \left (x^3+1\right )^{3/2}-\frac {2 \sqrt {x^3+1}}{3} \]
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Rubi [A] time = 0.01, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {266, 43} \[ \frac {2}{9} \left (x^3+1\right )^{3/2}-\frac {2 \sqrt {x^3+1}}{3} \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int \frac {x^5}{\sqrt {1+x^3}} \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int \frac {x}{\sqrt {1+x}} \, dx,x,x^3\right )\\ &=\frac {1}{3} \operatorname {Subst}\left (\int \left (-\frac {1}{\sqrt {1+x}}+\sqrt {1+x}\right ) \, dx,x,x^3\right )\\ &=-\frac {2}{3} \sqrt {1+x^3}+\frac {2}{9} \left (1+x^3\right )^{3/2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 18, normalized size = 0.67 \[ \frac {2}{9} \left (x^3-2\right ) \sqrt {x^3+1} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.67, size = 14, normalized size = 0.52 \[ \frac {2}{9} \, \sqrt {x^{3} + 1} {\left (x^{3} - 2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 19, normalized size = 0.70 \[ \frac {2}{9} \, {\left (x^{3} + 1\right )}^{\frac {3}{2}} - \frac {2}{3} \, \sqrt {x^{3} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 26, normalized size = 0.96 \[ \frac {2 \left (x +1\right ) \left (x^{2}-x +1\right ) \left (x^{3}-2\right )}{9 \sqrt {x^{3}+1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.32, size = 19, normalized size = 0.70 \[ \frac {2}{9} \, {\left (x^{3} + 1\right )}^{\frac {3}{2}} - \frac {2}{3} \, \sqrt {x^{3} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 14, normalized size = 0.52 \[ \frac {2\,\sqrt {x^3+1}\,\left (x^3-2\right )}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.39, size = 26, normalized size = 0.96 \[ \frac {2 x^{3} \sqrt {x^{3} + 1}}{9} - \frac {4 \sqrt {x^{3} + 1}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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