Optimal. Leaf size=53 \[ \frac{2}{21} \left (x^3+1\right )^{7/2}-\frac{2}{5} \left (x^3+1\right )^{5/2}+\frac{2}{3} \left (x^3+1\right )^{3/2}-\frac{2 \sqrt{x^3+1}}{3} \]
[Out]
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Rubi [A] time = 0.0481933, antiderivative size = 53, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{2}{21} \left (x^3+1\right )^{7/2}-\frac{2}{5} \left (x^3+1\right )^{5/2}+\frac{2}{3} \left (x^3+1\right )^{3/2}-\frac{2 \sqrt{x^3+1}}{3} \]
Antiderivative was successfully verified.
[In] Int[x^11/Sqrt[1 + x^3],x]
[Out]
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Rubi in Sympy [A] time = 5.04519, size = 46, normalized size = 0.87 \[ \frac{2 \left (x^{3} + 1\right )^{\frac{7}{2}}}{21} - \frac{2 \left (x^{3} + 1\right )^{\frac{5}{2}}}{5} + \frac{2 \left (x^{3} + 1\right )^{\frac{3}{2}}}{3} - \frac{2 \sqrt{x^{3} + 1}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**11/(x**3+1)**(1/2),x)
[Out]
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Mathematica [A] time = 0.015044, 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.
[In] Integrate[x^11/Sqrt[1 + x^3],x]
[Out]
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Maple [A] time = 0.008, size = 38, normalized size = 0.7 \[{\frac{ \left ( 2+2\,x \right ) \left ({x}^{2}-x+1 \right ) \left ( 5\,{x}^{9}-6\,{x}^{6}+8\,{x}^{3}-16 \right ) }{105}{\frac{1}{\sqrt{{x}^{3}+1}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^11/(x^3+1)^(1/2),x)
[Out]
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Maxima [A] time = 1.42324, size = 50, normalized size = 0.94 \[ \frac{2}{21} \,{\left (x^{3} + 1\right )}^{\frac{7}{2}} - \frac{2}{5} \,{\left (x^{3} + 1\right )}^{\frac{5}{2}} + \frac{2}{3} \,{\left (x^{3} + 1\right )}^{\frac{3}{2}} - \frac{2}{3} \, \sqrt{x^{3} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/sqrt(x^3 + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.231384, size = 35, normalized size = 0.66 \[ \frac{2}{105} \,{\left (5 \, x^{9} - 6 \, x^{6} + 8 \, x^{3} - 16\right )} \sqrt{x^{3} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/sqrt(x^3 + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.49298, 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.
[In] integrate(x**11/(x**3+1)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.241595, size = 50, normalized size = 0.94 \[ \frac{2}{21} \,{\left (x^{3} + 1\right )}^{\frac{7}{2}} - \frac{2}{5} \,{\left (x^{3} + 1\right )}^{\frac{5}{2}} + \frac{2}{3} \,{\left (x^{3} + 1\right )}^{\frac{3}{2}} - \frac{2}{3} \, \sqrt{x^{3} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/sqrt(x^3 + 1),x, algorithm="giac")
[Out]