Optimal. Leaf size=63 \[ \frac{2}{7} a^2 A x^{7/2}+\frac{2}{11} b x^{11/2} (2 a B+A b)+\frac{2}{9} a x^{9/2} (a B+2 A b)+\frac{2}{13} b^2 B x^{13/2} \]
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Rubi [A] time = 0.0829703, antiderivative size = 63, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ \frac{2}{7} a^2 A x^{7/2}+\frac{2}{11} b x^{11/2} (2 a B+A b)+\frac{2}{9} a x^{9/2} (a B+2 A b)+\frac{2}{13} b^2 B x^{13/2} \]
Antiderivative was successfully verified.
[In] Int[x^(5/2)*(a + b*x)^2*(A + B*x),x]
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Rubi in Sympy [A] time = 9.15124, size = 63, normalized size = 1. \[ \frac{2 A a^{2} x^{\frac{7}{2}}}{7} + \frac{2 B b^{2} x^{\frac{13}{2}}}{13} + \frac{2 a x^{\frac{9}{2}} \left (2 A b + B a\right )}{9} + \frac{2 b x^{\frac{11}{2}} \left (A b + 2 B a\right )}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(5/2)*(b*x+a)**2*(B*x+A),x)
[Out]
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Mathematica [A] time = 0.0272165, size = 52, normalized size = 0.83 \[ \frac{2 x^{7/2} \left (143 a^2 (9 A+7 B x)+182 a b x (11 A+9 B x)+63 b^2 x^2 (13 A+11 B x)\right )}{9009} \]
Antiderivative was successfully verified.
[In] Integrate[x^(5/2)*(a + b*x)^2*(A + B*x),x]
[Out]
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Maple [A] time = 0.008, size = 52, normalized size = 0.8 \[{\frac{1386\,B{b}^{2}{x}^{3}+1638\,A{b}^{2}{x}^{2}+3276\,B{x}^{2}ab+4004\,aAbx+2002\,{a}^{2}Bx+2574\,{a}^{2}A}{9009}{x}^{{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(5/2)*(b*x+a)^2*(B*x+A),x)
[Out]
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Maxima [A] time = 1.33361, size = 69, normalized size = 1.1 \[ \frac{2}{13} \, B b^{2} x^{\frac{13}{2}} + \frac{2}{7} \, A a^{2} x^{\frac{7}{2}} + \frac{2}{11} \,{\left (2 \, B a b + A b^{2}\right )} x^{\frac{11}{2}} + \frac{2}{9} \,{\left (B a^{2} + 2 \, A a b\right )} x^{\frac{9}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^2*x^(5/2),x, algorithm="maxima")
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Fricas [A] time = 0.206919, size = 76, normalized size = 1.21 \[ \frac{2}{9009} \,{\left (693 \, B b^{2} x^{6} + 1287 \, A a^{2} x^{3} + 819 \,{\left (2 \, B a b + A b^{2}\right )} x^{5} + 1001 \,{\left (B a^{2} + 2 \, A a b\right )} x^{4}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^2*x^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 10.3218, size = 80, normalized size = 1.27 \[ \frac{2 A a^{2} x^{\frac{7}{2}}}{7} + \frac{4 A a b x^{\frac{9}{2}}}{9} + \frac{2 A b^{2} x^{\frac{11}{2}}}{11} + \frac{2 B a^{2} x^{\frac{9}{2}}}{9} + \frac{4 B a b x^{\frac{11}{2}}}{11} + \frac{2 B b^{2} x^{\frac{13}{2}}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(5/2)*(b*x+a)**2*(B*x+A),x)
[Out]
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GIAC/XCAS [A] time = 0.270339, size = 72, normalized size = 1.14 \[ \frac{2}{13} \, B b^{2} x^{\frac{13}{2}} + \frac{4}{11} \, B a b x^{\frac{11}{2}} + \frac{2}{11} \, A b^{2} x^{\frac{11}{2}} + \frac{2}{9} \, B a^{2} x^{\frac{9}{2}} + \frac{4}{9} \, A a b x^{\frac{9}{2}} + \frac{2}{7} \, A a^{2} x^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^2*x^(5/2),x, algorithm="giac")
[Out]