Optimal. Leaf size=21 \[ \frac{2}{7} b x^{7/2}+\frac{2}{11} c x^{11/2} \]
[Out]
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Rubi [A] time = 0.0138933, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{2}{7} b x^{7/2}+\frac{2}{11} c x^{11/2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[x]*(b*x^2 + c*x^4),x]
[Out]
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Rubi in Sympy [A] time = 4.1029, size = 19, normalized size = 0.9 \[ \frac{2 b x^{\frac{7}{2}}}{7} + \frac{2 c x^{\frac{11}{2}}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(1/2)*(c*x**4+b*x**2),x)
[Out]
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Mathematica [A] time = 0.00761752, size = 21, normalized size = 1. \[ \frac{2}{7} b x^{7/2}+\frac{2}{11} c x^{11/2} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[x]*(b*x^2 + c*x^4),x]
[Out]
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Maple [A] time = 0.004, size = 16, normalized size = 0.8 \[{\frac{14\,c{x}^{2}+22\,b}{77}{x}^{{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(1/2)*(c*x^4+b*x^2),x)
[Out]
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Maxima [A] time = 0.734461, size = 18, normalized size = 0.86 \[ \frac{2}{11} \, c x^{\frac{11}{2}} + \frac{2}{7} \, b x^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)*sqrt(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.25727, size = 24, normalized size = 1.14 \[ \frac{2}{77} \,{\left (7 \, c x^{5} + 11 \, b x^{3}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)*sqrt(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.50547, size = 19, normalized size = 0.9 \[ \frac{2 b x^{\frac{7}{2}}}{7} + \frac{2 c x^{\frac{11}{2}}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(1/2)*(c*x**4+b*x**2),x)
[Out]
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GIAC/XCAS [A] time = 0.268264, size = 18, normalized size = 0.86 \[ \frac{2}{11} \, c x^{\frac{11}{2}} + \frac{2}{7} \, b x^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)*sqrt(x),x, algorithm="giac")
[Out]