Optimal. Leaf size=55 \[ \frac{2}{7} x^{7/2} (a B+A b)+\frac{2}{5} a A x^{5/2}+\frac{2}{9} x^{9/2} (A c+b B)+\frac{2}{11} B c x^{11/2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0674035, antiderivative size = 55, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048 \[ \frac{2}{7} x^{7/2} (a B+A b)+\frac{2}{5} a A x^{5/2}+\frac{2}{9} x^{9/2} (A c+b B)+\frac{2}{11} B c x^{11/2} \]
Antiderivative was successfully verified.
[In] Int[x^(3/2)*(A + B*x)*(a + b*x + c*x^2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 8.35434, size = 60, normalized size = 1.09 \[ \frac{2 A a x^{\frac{5}{2}}}{5} + \frac{2 B c x^{\frac{11}{2}}}{11} + x^{\frac{9}{2}} \left (\frac{2 A c}{9} + \frac{2 B b}{9}\right ) + x^{\frac{7}{2}} \left (\frac{2 A b}{7} + \frac{2 B a}{7}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(3/2)*(B*x+A)*(c*x**2+b*x+a),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0354052, size = 48, normalized size = 0.87 \[ \frac{2 x^{5/2} (99 a (7 A+5 B x)+5 x (11 A (9 b+7 c x)+7 B x (11 b+9 c x)))}{3465} \]
Antiderivative was successfully verified.
[In] Integrate[x^(3/2)*(A + B*x)*(a + b*x + c*x^2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.005, size = 42, normalized size = 0.8 \[{\frac{630\,Bc{x}^{3}+770\,Ac{x}^{2}+770\,Bb{x}^{2}+990\,Abx+990\,aBx+1386\,aA}{3465}{x}^{{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(3/2)*(B*x+A)*(c*x^2+b*x+a),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.711102, size = 53, normalized size = 0.96 \[ \frac{2}{11} \, B c x^{\frac{11}{2}} + \frac{2}{9} \,{\left (B b + A c\right )} x^{\frac{9}{2}} + \frac{2}{5} \, A a x^{\frac{5}{2}} + \frac{2}{7} \,{\left (B a + A b\right )} x^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A)*x^(3/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.281082, size = 59, normalized size = 1.07 \[ \frac{2}{3465} \,{\left (315 \, B c x^{5} + 385 \,{\left (B b + A c\right )} x^{4} + 693 \, A a x^{2} + 495 \,{\left (B a + A b\right )} x^{3}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A)*x^(3/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 3.74562, size = 70, normalized size = 1.27 \[ \frac{2 A a x^{\frac{5}{2}}}{5} + \frac{2 A b x^{\frac{7}{2}}}{7} + \frac{2 A c x^{\frac{9}{2}}}{9} + \frac{2 B a x^{\frac{7}{2}}}{7} + \frac{2 B b x^{\frac{9}{2}}}{9} + \frac{2 B c x^{\frac{11}{2}}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(3/2)*(B*x+A)*(c*x**2+b*x+a),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.270805, size = 58, normalized size = 1.05 \[ \frac{2}{11} \, B c x^{\frac{11}{2}} + \frac{2}{9} \, B b x^{\frac{9}{2}} + \frac{2}{9} \, A c x^{\frac{9}{2}} + \frac{2}{7} \, B a x^{\frac{7}{2}} + \frac{2}{7} \, A b x^{\frac{7}{2}} + \frac{2}{5} \, A a x^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A)*x^(3/2),x, algorithm="giac")
[Out]