Optimal. Leaf size=27 \[ \frac {1}{45} \sqrt {1-2 x^3} \left (6 x^6-x^3-1\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 31, normalized size of antiderivative = 1.15, number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {266, 43} \begin {gather*} \frac {1}{30} \left (1-2 x^3\right )^{5/2}-\frac {1}{18} \left (1-2 x^3\right )^{3/2} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int x^5 \sqrt {1-2 x^3} \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int \sqrt {1-2 x} x \, dx,x,x^3\right )\\ &=\frac {1}{3} \operatorname {Subst}\left (\int \left (\frac {1}{2} \sqrt {1-2 x}-\frac {1}{2} (1-2 x)^{3/2}\right ) \, dx,x,x^3\right )\\ &=-\frac {1}{18} \left (1-2 x^3\right )^{3/2}+\frac {1}{30} \left (1-2 x^3\right )^{5/2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 22, normalized size = 0.81 \begin {gather*} -\frac {1}{45} \left (1-2 x^3\right )^{3/2} \left (3 x^3+1\right ) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 22, normalized size = 0.81 \begin {gather*} \frac {1}{45} \left (-1-3 x^3\right ) \left (1-2 x^3\right )^{3/2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.45, size = 23, normalized size = 0.85 \begin {gather*} \frac {1}{45} \, {\left (6 \, x^{6} - x^{3} - 1\right )} \sqrt {-2 \, x^{3} + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.31, size = 32, normalized size = 1.19 \begin {gather*} \frac {1}{30} \, {\left (2 \, x^{3} - 1\right )}^{2} \sqrt {-2 \, x^{3} + 1} - \frac {1}{18} \, {\left (-2 \, x^{3} + 1\right )}^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.13, size = 19, normalized size = 0.70
method | result | size |
gosper | \(-\frac {\left (3 x^{3}+1\right ) \left (-2 x^{3}+1\right )^{\frac {3}{2}}}{45}\) | \(19\) |
trager | \(\left (\frac {2}{15} x^{6}-\frac {1}{45} x^{3}-\frac {1}{45}\right ) \sqrt {-2 x^{3}+1}\) | \(23\) |
risch | \(-\frac {\left (6 x^{6}-x^{3}-1\right ) \left (2 x^{3}-1\right )}{45 \sqrt {-2 x^{3}+1}}\) | \(31\) |
meijerg | \(-\frac {-\frac {8 \sqrt {\pi }}{15}+\frac {4 \sqrt {\pi }\, \left (-2 x^{3}+1\right )^{\frac {3}{2}} \left (6 x^{3}+2\right )}{15}}{24 \sqrt {\pi }}\) | \(33\) |
default | \(\frac {2 x^{6} \sqrt {-2 x^{3}+1}}{15}-\frac {x^{3} \sqrt {-2 x^{3}+1}}{45}-\frac {\sqrt {-2 x^{3}+1}}{45}\) | \(41\) |
elliptic | \(\frac {2 x^{6} \sqrt {-2 x^{3}+1}}{15}-\frac {x^{3} \sqrt {-2 x^{3}+1}}{45}-\frac {\sqrt {-2 x^{3}+1}}{45}\) | \(41\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.32, size = 23, normalized size = 0.85 \begin {gather*} \frac {1}{30} \, {\left (-2 \, x^{3} + 1\right )}^{\frac {5}{2}} - \frac {1}{18} \, {\left (-2 \, x^{3} + 1\right )}^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.15, size = 34, normalized size = 1.26 \begin {gather*} -\frac {\frac {5\,{\left (2\,x^3-1\right )}^2}{2}+\frac {3\,{\left (2\,x^3-1\right )}^3}{2}}{45\,\sqrt {1-2\,x^3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.29, size = 42, normalized size = 1.56 \begin {gather*} \frac {2 x^{6} \sqrt {1 - 2 x^{3}}}{15} - \frac {x^{3} \sqrt {1 - 2 x^{3}}}{45} - \frac {\sqrt {1 - 2 x^{3}}}{45} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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