Optimal. Leaf size=111 \[ \frac{2}{7} a^4 A x^{7/2}+\frac{2}{9} a^3 x^{9/2} (a B+4 A b)+\frac{4}{11} a^2 b x^{11/2} (2 a B+3 A b)+\frac{2}{15} b^3 x^{15/2} (4 a B+A b)+\frac{4}{13} a b^2 x^{13/2} (3 a B+2 A b)+\frac{2}{17} b^4 B x^{17/2} \]
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Rubi [A] time = 0.135482, antiderivative size = 111, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 29, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.069 \[ \frac{2}{7} a^4 A x^{7/2}+\frac{2}{9} a^3 x^{9/2} (a B+4 A b)+\frac{4}{11} a^2 b x^{11/2} (2 a B+3 A b)+\frac{2}{15} b^3 x^{15/2} (4 a B+A b)+\frac{4}{13} a b^2 x^{13/2} (3 a B+2 A b)+\frac{2}{17} b^4 B x^{17/2} \]
Antiderivative was successfully verified.
[In] Int[x^(5/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]
[Out]
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Rubi in Sympy [A] time = 31.9675, size = 114, normalized size = 1.03 \[ \frac{2 A a^{4} x^{\frac{7}{2}}}{7} + \frac{2 B b^{4} x^{\frac{17}{2}}}{17} + \frac{2 a^{3} x^{\frac{9}{2}} \left (4 A b + B a\right )}{9} + \frac{4 a^{2} b x^{\frac{11}{2}} \left (3 A b + 2 B a\right )}{11} + \frac{4 a b^{2} x^{\frac{13}{2}} \left (2 A b + 3 B a\right )}{13} + \frac{2 b^{3} x^{\frac{15}{2}} \left (A b + 4 B a\right )}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(5/2)*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2,x)
[Out]
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Mathematica [A] time = 0.0499356, size = 111, normalized size = 1. \[ \frac{2}{7} a^4 A x^{7/2}+\frac{2}{9} a^3 x^{9/2} (a B+4 A b)+\frac{4}{11} a^2 b x^{11/2} (2 a B+3 A b)+\frac{2}{15} b^3 x^{15/2} (4 a B+A b)+\frac{4}{13} a b^2 x^{13/2} (3 a B+2 A b)+\frac{2}{17} b^4 B x^{17/2} \]
Antiderivative was successfully verified.
[In] Integrate[x^(5/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]
[Out]
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Maple [A] time = 0.011, size = 100, normalized size = 0.9 \[{\frac{90090\,{b}^{4}B{x}^{5}+102102\,A{b}^{4}{x}^{4}+408408\,B{x}^{4}a{b}^{3}+471240\,aA{b}^{3}{x}^{3}+706860\,B{x}^{3}{a}^{2}{b}^{2}+835380\,{a}^{2}A{b}^{2}{x}^{2}+556920\,B{x}^{2}{a}^{3}b+680680\,{a}^{3}Abx+170170\,{a}^{4}Bx+218790\,A{a}^{4}}{765765}{x}^{{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(5/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2,x)
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Maxima [A] time = 0.689057, size = 134, normalized size = 1.21 \[ \frac{2}{17} \, B b^{4} x^{\frac{17}{2}} + \frac{2}{7} \, A a^{4} x^{\frac{7}{2}} + \frac{2}{15} \,{\left (4 \, B a b^{3} + A b^{4}\right )} x^{\frac{15}{2}} + \frac{4}{13} \,{\left (3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right )} x^{\frac{13}{2}} + \frac{4}{11} \,{\left (2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right )} x^{\frac{11}{2}} + \frac{2}{9} \,{\left (B a^{4} + 4 \, A a^{3} b\right )} x^{\frac{9}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)^2*(B*x + A)*x^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.275563, size = 140, normalized size = 1.26 \[ \frac{2}{765765} \,{\left (45045 \, B b^{4} x^{8} + 109395 \, A a^{4} x^{3} + 51051 \,{\left (4 \, B a b^{3} + A b^{4}\right )} x^{7} + 117810 \,{\left (3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right )} x^{6} + 139230 \,{\left (2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right )} x^{5} + 85085 \,{\left (B a^{4} + 4 \, A a^{3} b\right )} x^{4}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)^2*(B*x + A)*x^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 23.3753, size = 148, normalized size = 1.33 \[ \frac{2 A a^{4} x^{\frac{7}{2}}}{7} + \frac{8 A a^{3} b x^{\frac{9}{2}}}{9} + \frac{12 A a^{2} b^{2} x^{\frac{11}{2}}}{11} + \frac{8 A a b^{3} x^{\frac{13}{2}}}{13} + \frac{2 A b^{4} x^{\frac{15}{2}}}{15} + \frac{2 B a^{4} x^{\frac{9}{2}}}{9} + \frac{8 B a^{3} b x^{\frac{11}{2}}}{11} + \frac{12 B a^{2} b^{2} x^{\frac{13}{2}}}{13} + \frac{8 B a b^{3} x^{\frac{15}{2}}}{15} + \frac{2 B b^{4} x^{\frac{17}{2}}}{17} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(5/2)*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.272784, size = 136, normalized size = 1.23 \[ \frac{2}{17} \, B b^{4} x^{\frac{17}{2}} + \frac{8}{15} \, B a b^{3} x^{\frac{15}{2}} + \frac{2}{15} \, A b^{4} x^{\frac{15}{2}} + \frac{12}{13} \, B a^{2} b^{2} x^{\frac{13}{2}} + \frac{8}{13} \, A a b^{3} x^{\frac{13}{2}} + \frac{8}{11} \, B a^{3} b x^{\frac{11}{2}} + \frac{12}{11} \, A a^{2} b^{2} x^{\frac{11}{2}} + \frac{2}{9} \, B a^{4} x^{\frac{9}{2}} + \frac{8}{9} \, A a^{3} b x^{\frac{9}{2}} + \frac{2}{7} \, A a^{4} x^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)^2*(B*x + A)*x^(5/2),x, algorithm="giac")
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