Optimal. Leaf size=53 \[ \frac {2}{21} \left (x^3+1\right )^{7/2}-\frac {2}{5} \left (x^3+1\right )^{5/2}+\frac {2}{3} \left (x^3+1\right )^{3/2}-\frac {2 \sqrt {x^3+1}}{3} \]
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Rubi [A] time = 0.02, antiderivative size = 53, 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} \[ \frac {2}{21} \left (x^3+1\right )^{7/2}-\frac {2}{5} \left (x^3+1\right )^{5/2}+\frac {2}{3} \left (x^3+1\right )^{3/2}-\frac {2 \sqrt {x^3+1}}{3} \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int \frac {x^{11}}{\sqrt {1+x^3}} \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int \frac {x^3}{\sqrt {1+x}} \, dx,x,x^3\right )\\ &=\frac {1}{3} \operatorname {Subst}\left (\int \left (-\frac {1}{\sqrt {1+x}}+3 \sqrt {1+x}-3 (1+x)^{3/2}+(1+x)^{5/2}\right ) \, dx,x,x^3\right )\\ &=-\frac {2}{3} \sqrt {1+x^3}+\frac {2}{3} \left (1+x^3\right )^{3/2}-\frac {2}{5} \left (1+x^3\right )^{5/2}+\frac {2}{21} \left (1+x^3\right )^{7/2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 30, normalized size = 0.57 \[ \frac {2}{105} \sqrt {x^3+1} \left (5 x^9-6 x^6+8 x^3-16\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.72, size = 26, normalized size = 0.49 \[ \frac {2}{105} \, {\left (5 \, x^{9} - 6 \, x^{6} + 8 \, x^{3} - 16\right )} \sqrt {x^{3} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 37, normalized size = 0.70 \[ \frac {2}{21} \, {\left (x^{3} + 1\right )}^{\frac {7}{2}} - \frac {2}{5} \, {\left (x^{3} + 1\right )}^{\frac {5}{2}} + \frac {2}{3} \, {\left (x^{3} + 1\right )}^{\frac {3}{2}} - \frac {2}{3} \, \sqrt {x^{3} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 38, normalized size = 0.72 \[ \frac {2 \left (x +1\right ) \left (x^{2}-x +1\right ) \left (5 x^{9}-6 x^{6}+8 x^{3}-16\right )}{105 \sqrt {x^{3}+1}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.36, size = 37, normalized size = 0.70 \[ \frac {2}{21} \, {\left (x^{3} + 1\right )}^{\frac {7}{2}} - \frac {2}{5} \, {\left (x^{3} + 1\right )}^{\frac {5}{2}} + \frac {2}{3} \, {\left (x^{3} + 1\right )}^{\frac {3}{2}} - \frac {2}{3} \, \sqrt {x^{3} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.00, size = 46, normalized size = 0.87 \[ \frac {16\,x^3\,\sqrt {x^3+1}}{105}-\frac {32\,\sqrt {x^3+1}}{105}-\frac {4\,x^6\,\sqrt {x^3+1}}{35}+\frac {2\,x^9\,\sqrt {x^3+1}}{21} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.91, size = 56, normalized size = 1.06 \[ \frac {2 x^{9} \sqrt {x^{3} + 1}}{21} - \frac {4 x^{6} \sqrt {x^{3} + 1}}{35} + \frac {16 x^{3} \sqrt {x^{3} + 1}}{105} - \frac {32 \sqrt {x^{3} + 1}}{105} \]
Verification of antiderivative is not currently implemented for this CAS.
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