Optimal. Leaf size=19 \[ \frac{2 x^{7/2}}{7}+\frac{2 x^{3/2}}{3} \]
[Out]
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Rubi [A] time = 0.00736761, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{2 x^{7/2}}{7}+\frac{2 x^{3/2}}{3} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[x]*(1 + x^2),x]
[Out]
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Rubi in Sympy [A] time = 0.976133, size = 15, normalized size = 0.79 \[ \frac{2 x^{\frac{7}{2}}}{7} + \frac{2 x^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(1/2)*(x**2+1),x)
[Out]
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Mathematica [A] time = 0.00417738, size = 16, normalized size = 0.84 \[ \frac{2}{21} x^{3/2} \left (3 x^2+7\right ) \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[x]*(1 + x^2),x]
[Out]
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Maple [A] time = 0.002, size = 13, normalized size = 0.7 \[{\frac{6\,{x}^{2}+14}{21}{x}^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(1/2)*(x^2+1),x)
[Out]
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Maxima [A] time = 1.36906, size = 15, normalized size = 0.79 \[ \frac{2}{7} \, x^{\frac{7}{2}} + \frac{2}{3} \, x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 1)*sqrt(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.221029, size = 19, normalized size = 1. \[ \frac{2}{21} \,{\left (3 \, x^{3} + 7 \, x\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 1)*sqrt(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.66284, size = 15, normalized size = 0.79 \[ \frac{2 x^{\frac{7}{2}}}{7} + \frac{2 x^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(1/2)*(x**2+1),x)
[Out]
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GIAC/XCAS [A] time = 0.201137, size = 15, normalized size = 0.79 \[ \frac{2}{7} \, x^{\frac{7}{2}} + \frac{2}{3} \, x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 1)*sqrt(x),x, algorithm="giac")
[Out]