Optimal. Leaf size=63 \[ \frac{2}{9} a^2 A x^{9/2}+\frac{2}{13} b x^{13/2} (2 a B+A b)+\frac{2}{11} a x^{11/2} (a B+2 A b)+\frac{2}{15} b^2 B x^{15/2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0831956, antiderivative size = 63, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 27, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.074 \[ \frac{2}{9} a^2 A x^{9/2}+\frac{2}{13} b x^{13/2} (2 a B+A b)+\frac{2}{11} a x^{11/2} (a B+2 A b)+\frac{2}{15} b^2 B x^{15/2} \]
Antiderivative was successfully verified.
[In] Int[x^(7/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 19.4682, size = 63, normalized size = 1. \[ \frac{2 A a^{2} x^{\frac{9}{2}}}{9} + \frac{2 B b^{2} x^{\frac{15}{2}}}{15} + \frac{2 a x^{\frac{11}{2}} \left (2 A b + B a\right )}{11} + \frac{2 b x^{\frac{13}{2}} \left (A b + 2 B a\right )}{13} \]
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),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0361859, size = 51, normalized size = 0.81 \[ \frac{2 x^{9/2} \left (715 a^2 A+495 b x^2 (2 a B+A b)+585 a x (a B+2 A b)+429 b^2 B x^3\right )}{6435} \]
Antiderivative was successfully verified.
[In] Integrate[x^(7/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2),x]
[Out]
_______________________________________________________________________________________
Maple [F] time = 180., size = 0, normalized size = 0. \[ \text{hanged} \]
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),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.713635, size = 69, normalized size = 1.1 \[ \frac{2}{15} \, B b^{2} x^{\frac{15}{2}} + \frac{2}{9} \, A a^{2} x^{\frac{9}{2}} + \frac{2}{13} \,{\left (2 \, B a b + A b^{2}\right )} x^{\frac{13}{2}} + \frac{2}{11} \,{\left (B a^{2} + 2 \, A a b\right )} x^{\frac{11}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)*(B*x + A)*x^(7/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.288438, size = 76, normalized size = 1.21 \[ \frac{2}{6435} \,{\left (429 \, B b^{2} x^{7} + 715 \, A a^{2} x^{4} + 495 \,{\left (2 \, B a b + A b^{2}\right )} x^{6} + 585 \,{\left (B a^{2} + 2 \, A a b\right )} x^{5}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)*(B*x + A)*x^(7/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 21.0089, size = 80, normalized size = 1.27 \[ \frac{2 A a^{2} x^{\frac{9}{2}}}{9} + \frac{4 A a b x^{\frac{11}{2}}}{11} + \frac{2 A b^{2} x^{\frac{13}{2}}}{13} + \frac{2 B a^{2} x^{\frac{11}{2}}}{11} + \frac{4 B a b x^{\frac{13}{2}}}{13} + \frac{2 B b^{2} x^{\frac{15}{2}}}{15} \]
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),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.268951, size = 72, normalized size = 1.14 \[ \frac{2}{15} \, B b^{2} x^{\frac{15}{2}} + \frac{4}{13} \, B a b x^{\frac{13}{2}} + \frac{2}{13} \, A b^{2} x^{\frac{13}{2}} + \frac{2}{11} \, B a^{2} x^{\frac{11}{2}} + \frac{4}{11} \, A a b x^{\frac{11}{2}} + \frac{2}{9} \, A a^{2} x^{\frac{9}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)*(B*x + A)*x^(7/2),x, algorithm="giac")
[Out]