Optimal. Leaf size=109 \[ \frac{2}{9} a^3 A x^{9/2}+\frac{2}{11} a^3 B x^{11/2}+\frac{6}{13} a^2 A c x^{13/2}+\frac{2}{5} a^2 B c x^{15/2}+\frac{6}{17} a A c^2 x^{17/2}+\frac{6}{19} a B c^2 x^{19/2}+\frac{2}{21} A c^3 x^{21/2}+\frac{2}{23} B c^3 x^{23/2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.101694, antiderivative size = 109, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{2}{9} a^3 A x^{9/2}+\frac{2}{11} a^3 B x^{11/2}+\frac{6}{13} a^2 A c x^{13/2}+\frac{2}{5} a^2 B c x^{15/2}+\frac{6}{17} a A c^2 x^{17/2}+\frac{6}{19} a B c^2 x^{19/2}+\frac{2}{21} A c^3 x^{21/2}+\frac{2}{23} B c^3 x^{23/2} \]
Antiderivative was successfully verified.
[In] Int[x^(7/2)*(A + B*x)*(a + c*x^2)^3,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 11.4405, size = 114, normalized size = 1.05 \[ \frac{2 A a^{3} x^{\frac{9}{2}}}{9} + \frac{6 A a^{2} c x^{\frac{13}{2}}}{13} + \frac{6 A a c^{2} x^{\frac{17}{2}}}{17} + \frac{2 A c^{3} x^{\frac{21}{2}}}{21} + \frac{2 B a^{3} x^{\frac{11}{2}}}{11} + \frac{2 B a^{2} c x^{\frac{15}{2}}}{5} + \frac{6 B a c^{2} x^{\frac{19}{2}}}{19} + \frac{2 B c^{3} x^{\frac{23}{2}}}{23} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(7/2)*(B*x+A)*(c*x**2+a)**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0559945, size = 83, normalized size = 0.76 \[ \frac{2}{99} a^3 x^{9/2} (11 A+9 B x)+\frac{2}{65} a^2 c x^{13/2} (15 A+13 B x)+\frac{6}{323} a c^2 x^{17/2} (19 A+17 B x)+\frac{2}{483} c^3 x^{21/2} (23 A+21 B x) \]
Antiderivative was successfully verified.
[In] Integrate[x^(7/2)*(A + B*x)*(a + c*x^2)^3,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.01, size = 78, normalized size = 0.7 \[{\frac{29099070\,B{c}^{3}{x}^{7}+31870410\,A{c}^{3}{x}^{6}+105675570\,aB{c}^{2}{x}^{5}+118107990\,aA{c}^{2}{x}^{4}+133855722\,{a}^{2}Bc{x}^{3}+154448910\,{a}^{2}Ac{x}^{2}+60843510\,{a}^{3}Bx+74364290\,A{a}^{3}}{334639305}{x}^{{\frac{9}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(7/2)*(B*x+A)*(c*x^2+a)^3,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.686555, size = 104, normalized size = 0.95 \[ \frac{2}{23} \, B c^{3} x^{\frac{23}{2}} + \frac{2}{21} \, A c^{3} x^{\frac{21}{2}} + \frac{6}{19} \, B a c^{2} x^{\frac{19}{2}} + \frac{6}{17} \, A a c^{2} x^{\frac{17}{2}} + \frac{2}{5} \, B a^{2} c x^{\frac{15}{2}} + \frac{6}{13} \, A a^{2} c x^{\frac{13}{2}} + \frac{2}{11} \, B a^{3} x^{\frac{11}{2}} + \frac{2}{9} \, A a^{3} x^{\frac{9}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)^3*(B*x + A)*x^(7/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.265505, size = 111, normalized size = 1.02 \[ \frac{2}{334639305} \,{\left (14549535 \, B c^{3} x^{11} + 15935205 \, A c^{3} x^{10} + 52837785 \, B a c^{2} x^{9} + 59053995 \, A a c^{2} x^{8} + 66927861 \, B a^{2} c x^{7} + 77224455 \, A a^{2} c x^{6} + 30421755 \, B a^{3} x^{5} + 37182145 \, A a^{3} x^{4}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)^3*(B*x + A)*x^(7/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 76.7794, size = 114, normalized size = 1.05 \[ \frac{2 A a^{3} x^{\frac{9}{2}}}{9} + \frac{6 A a^{2} c x^{\frac{13}{2}}}{13} + \frac{6 A a c^{2} x^{\frac{17}{2}}}{17} + \frac{2 A c^{3} x^{\frac{21}{2}}}{21} + \frac{2 B a^{3} x^{\frac{11}{2}}}{11} + \frac{2 B a^{2} c x^{\frac{15}{2}}}{5} + \frac{6 B a c^{2} x^{\frac{19}{2}}}{19} + \frac{2 B c^{3} x^{\frac{23}{2}}}{23} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(7/2)*(B*x+A)*(c*x**2+a)**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.2685, size = 104, normalized size = 0.95 \[ \frac{2}{23} \, B c^{3} x^{\frac{23}{2}} + \frac{2}{21} \, A c^{3} x^{\frac{21}{2}} + \frac{6}{19} \, B a c^{2} x^{\frac{19}{2}} + \frac{6}{17} \, A a c^{2} x^{\frac{17}{2}} + \frac{2}{5} \, B a^{2} c x^{\frac{15}{2}} + \frac{6}{13} \, A a^{2} c x^{\frac{13}{2}} + \frac{2}{11} \, B a^{3} x^{\frac{11}{2}} + \frac{2}{9} \, A a^{3} x^{\frac{9}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)^3*(B*x + A)*x^(7/2),x, algorithm="giac")
[Out]