Optimal. Leaf size=40 \[ \frac{1}{10} \left (x^4+1\right )^{5/2}-\frac{1}{3} \left (x^4+1\right )^{3/2}+\frac{\sqrt{x^4+1}}{2} \]
[Out]
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Rubi [A] time = 0.0412065, antiderivative size = 40, 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 \[ \frac{1}{10} \left (x^4+1\right )^{5/2}-\frac{1}{3} \left (x^4+1\right )^{3/2}+\frac{\sqrt{x^4+1}}{2} \]
Antiderivative was successfully verified.
[In] Int[x^11/Sqrt[1 + x^4],x]
[Out]
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Rubi in Sympy [A] time = 4.11713, size = 29, normalized size = 0.72 \[ \frac{\left (x^{4} + 1\right )^{\frac{5}{2}}}{10} - \frac{\left (x^{4} + 1\right )^{\frac{3}{2}}}{3} + \frac{\sqrt{x^{4} + 1}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**11/(x**4+1)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0147247, size = 25, normalized size = 0.62 \[ \frac{1}{30} \sqrt{x^4+1} \left (3 x^8-4 x^4+8\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^11/Sqrt[1 + x^4],x]
[Out]
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Maple [A] time = 0.006, size = 22, normalized size = 0.6 \[{\frac{3\,{x}^{8}-4\,{x}^{4}+8}{30}\sqrt{{x}^{4}+1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^11/(x^4+1)^(1/2),x)
[Out]
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Maxima [A] time = 1.43604, size = 38, normalized size = 0.95 \[ \frac{1}{10} \,{\left (x^{4} + 1\right )}^{\frac{5}{2}} - \frac{1}{3} \,{\left (x^{4} + 1\right )}^{\frac{3}{2}} + \frac{1}{2} \, \sqrt{x^{4} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/sqrt(x^4 + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.265958, size = 28, normalized size = 0.7 \[ \frac{1}{30} \,{\left (3 \, x^{8} - 4 \, x^{4} + 8\right )} \sqrt{x^{4} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/sqrt(x^4 + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.08776, size = 39, normalized size = 0.98 \[ \frac{x^{8} \sqrt{x^{4} + 1}}{10} - \frac{2 x^{4} \sqrt{x^{4} + 1}}{15} + \frac{4 \sqrt{x^{4} + 1}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**11/(x**4+1)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.213109, size = 38, normalized size = 0.95 \[ \frac{1}{10} \,{\left (x^{4} + 1\right )}^{\frac{5}{2}} - \frac{1}{3} \,{\left (x^{4} + 1\right )}^{\frac{3}{2}} + \frac{1}{2} \, \sqrt{x^{4} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/sqrt(x^4 + 1),x, algorithm="giac")
[Out]