Optimal. Leaf size=111 \[ \frac{2}{9} a^4 A x^{9/2}+\frac{2}{11} a^3 x^{11/2} (a B+4 A b)+\frac{4}{13} a^2 b x^{13/2} (2 a B+3 A b)+\frac{2}{17} b^3 x^{17/2} (4 a B+A b)+\frac{4}{15} a b^2 x^{15/2} (3 a B+2 A b)+\frac{2}{19} b^4 B x^{19/2} \]
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Rubi [A] time = 0.142881, 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 \[ \frac{2}{9} a^4 A x^{9/2}+\frac{2}{11} a^3 x^{11/2} (a B+4 A b)+\frac{4}{13} a^2 b x^{13/2} (2 a B+3 A b)+\frac{2}{17} b^3 x^{17/2} (4 a B+A b)+\frac{4}{15} a b^2 x^{15/2} (3 a B+2 A b)+\frac{2}{19} b^4 B x^{19/2} \]
Antiderivative was successfully verified.
[In] Int[x^(7/2)*(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 = 31.8972, size = 114, normalized size = 1.03 \[ \frac{2 A a^{4} x^{\frac{9}{2}}}{9} + \frac{2 B b^{4} x^{\frac{19}{2}}}{19} + \frac{2 a^{3} x^{\frac{11}{2}} \left (4 A b + B a\right )}{11} + \frac{4 a^{2} b x^{\frac{13}{2}} \left (3 A b + 2 B a\right )}{13} + \frac{4 a b^{2} x^{\frac{15}{2}} \left (2 A b + 3 B a\right )}{15} + \frac{2 b^{3} x^{\frac{17}{2}} \left (A b + 4 B a\right )}{17} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(7/2)*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2,x)
[Out]
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Mathematica [A] time = 0.0549395, size = 111, normalized size = 1. \[ \frac{2}{9} a^4 A x^{9/2}+\frac{2}{11} a^3 x^{11/2} (a B+4 A b)+\frac{4}{13} a^2 b x^{13/2} (2 a B+3 A b)+\frac{2}{17} b^3 x^{17/2} (4 a B+A b)+\frac{4}{15} a b^2 x^{15/2} (3 a B+2 A b)+\frac{2}{19} b^4 B x^{19/2} \]
Antiderivative was successfully verified.
[In] Integrate[x^(7/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]
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Maple [A] time = 0.011, size = 100, normalized size = 0.9 \[{\frac{218790\,{b}^{4}B{x}^{5}+244530\,A{b}^{4}{x}^{4}+978120\,B{x}^{4}a{b}^{3}+1108536\,aA{b}^{3}{x}^{3}+1662804\,B{x}^{3}{a}^{2}{b}^{2}+1918620\,{a}^{2}A{b}^{2}{x}^{2}+1279080\,B{x}^{2}{a}^{3}b+1511640\,{a}^{3}Abx+377910\,{a}^{4}Bx+461890\,A{a}^{4}}{2078505}{x}^{{\frac{9}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(7/2)*(B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2,x)
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Maxima [A] time = 0.68642, size = 134, normalized size = 1.21 \[ \frac{2}{19} \, B b^{4} x^{\frac{19}{2}} + \frac{2}{9} \, A a^{4} x^{\frac{9}{2}} + \frac{2}{17} \,{\left (4 \, B a b^{3} + A b^{4}\right )} x^{\frac{17}{2}} + \frac{4}{15} \,{\left (3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right )} x^{\frac{15}{2}} + \frac{4}{13} \,{\left (2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right )} x^{\frac{13}{2}} + \frac{2}{11} \,{\left (B a^{4} + 4 \, A a^{3} b\right )} x^{\frac{11}{2}} \]
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^(7/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.277098, size = 140, normalized size = 1.26 \[ \frac{2}{2078505} \,{\left (109395 \, B b^{4} x^{9} + 230945 \, A a^{4} x^{4} + 122265 \,{\left (4 \, B a b^{3} + A b^{4}\right )} x^{8} + 277134 \,{\left (3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right )} x^{7} + 319770 \,{\left (2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right )} x^{6} + 188955 \,{\left (B a^{4} + 4 \, A a^{3} b\right )} x^{5}\right )} \sqrt{x} \]
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^(7/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 46.062, size = 148, normalized size = 1.33 \[ \frac{2 A a^{4} x^{\frac{9}{2}}}{9} + \frac{8 A a^{3} b x^{\frac{11}{2}}}{11} + \frac{12 A a^{2} b^{2} x^{\frac{13}{2}}}{13} + \frac{8 A a b^{3} x^{\frac{15}{2}}}{15} + \frac{2 A b^{4} x^{\frac{17}{2}}}{17} + \frac{2 B a^{4} x^{\frac{11}{2}}}{11} + \frac{8 B a^{3} b x^{\frac{13}{2}}}{13} + \frac{4 B a^{2} b^{2} x^{\frac{15}{2}}}{5} + \frac{8 B a b^{3} x^{\frac{17}{2}}}{17} + \frac{2 B b^{4} x^{\frac{19}{2}}}{19} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(7/2)*(B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2,x)
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GIAC/XCAS [A] time = 0.267338, size = 136, normalized size = 1.23 \[ \frac{2}{19} \, B b^{4} x^{\frac{19}{2}} + \frac{8}{17} \, B a b^{3} x^{\frac{17}{2}} + \frac{2}{17} \, A b^{4} x^{\frac{17}{2}} + \frac{4}{5} \, B a^{2} b^{2} x^{\frac{15}{2}} + \frac{8}{15} \, A a b^{3} x^{\frac{15}{2}} + \frac{8}{13} \, B a^{3} b x^{\frac{13}{2}} + \frac{12}{13} \, A a^{2} b^{2} x^{\frac{13}{2}} + \frac{2}{11} \, B a^{4} x^{\frac{11}{2}} + \frac{8}{11} \, A a^{3} b x^{\frac{11}{2}} + \frac{2}{9} \, A a^{4} x^{\frac{9}{2}} \]
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^(7/2),x, algorithm="giac")
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