Optimal. Leaf size=36 \[ \frac{2}{7} a^2 x^{7/2}+\frac{4}{9} a b x^{9/2}+\frac{2}{11} b^2 x^{11/2} \]
[Out]
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Rubi [A] time = 0.0219416, antiderivative size = 36, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{2}{7} a^2 x^{7/2}+\frac{4}{9} a b x^{9/2}+\frac{2}{11} b^2 x^{11/2} \]
Antiderivative was successfully verified.
[In] Int[x^(5/2)*(a + b*x)^2,x]
[Out]
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Rubi in Sympy [A] time = 3.90524, size = 34, normalized size = 0.94 \[ \frac{2 a^{2} x^{\frac{7}{2}}}{7} + \frac{4 a b x^{\frac{9}{2}}}{9} + \frac{2 b^{2} x^{\frac{11}{2}}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(5/2)*(b*x+a)**2,x)
[Out]
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Mathematica [A] time = 0.00914127, size = 28, normalized size = 0.78 \[ \frac{2}{693} x^{7/2} \left (99 a^2+154 a b x+63 b^2 x^2\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^(5/2)*(a + b*x)^2,x]
[Out]
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Maple [A] time = 0.007, size = 25, normalized size = 0.7 \[{\frac{126\,{b}^{2}{x}^{2}+308\,abx+198\,{a}^{2}}{693}{x}^{{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(5/2)*(b*x+a)^2,x)
[Out]
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Maxima [A] time = 1.34051, size = 32, normalized size = 0.89 \[ \frac{2}{11} \, b^{2} x^{\frac{11}{2}} + \frac{4}{9} \, a b x^{\frac{9}{2}} + \frac{2}{7} \, a^{2} x^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^2*x^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.207593, size = 39, normalized size = 1.08 \[ \frac{2}{693} \,{\left (63 \, b^{2} x^{5} + 154 \, a b x^{4} + 99 \, a^{2} x^{3}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^2*x^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.09984, size = 34, normalized size = 0.94 \[ \frac{2 a^{2} x^{\frac{7}{2}}}{7} + \frac{4 a b x^{\frac{9}{2}}}{9} + \frac{2 b^{2} x^{\frac{11}{2}}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(5/2)*(b*x+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.203648, size = 32, normalized size = 0.89 \[ \frac{2}{11} \, b^{2} x^{\frac{11}{2}} + \frac{4}{9} \, a b x^{\frac{9}{2}} + \frac{2}{7} \, a^{2} x^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^2*x^(5/2),x, algorithm="giac")
[Out]