Optimal. Leaf size=39 \[ \frac{2}{5} x^{5/2} (a B+A b)+\frac{2}{3} a A x^{3/2}+\frac{2}{7} b B x^{7/2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0419955, antiderivative size = 39, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ \frac{2}{5} x^{5/2} (a B+A b)+\frac{2}{3} a A x^{3/2}+\frac{2}{7} b B x^{7/2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[x]*(a + b*x)*(A + B*x),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.17717, size = 41, normalized size = 1.05 \[ \frac{2 A a x^{\frac{3}{2}}}{3} + \frac{2 B b x^{\frac{7}{2}}}{7} + x^{\frac{5}{2}} \left (\frac{2 A b}{5} + \frac{2 B a}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(B*x+A)*x**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0157931, size = 33, normalized size = 0.85 \[ \frac{2}{105} x^{3/2} (7 a (5 A+3 B x)+3 b x (7 A+5 B x)) \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[x]*(a + b*x)*(A + B*x),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.006, size = 28, normalized size = 0.7 \[{\frac{30\,bB{x}^{2}+42\,Abx+42\,Bax+70\,Aa}{105}{x}^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(B*x+A)*x^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.35339, size = 36, normalized size = 0.92 \[ \frac{2}{7} \, B b x^{\frac{7}{2}} + \frac{2}{3} \, A a x^{\frac{3}{2}} + \frac{2}{5} \,{\left (B a + A b\right )} x^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)*sqrt(x),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.205526, size = 41, normalized size = 1.05 \[ \frac{2}{105} \,{\left (15 \, B b x^{3} + 35 \, A a x + 21 \,{\left (B a + A b\right )} x^{2}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)*sqrt(x),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 4.2038, size = 37, normalized size = 0.95 \[ \frac{2 A a x^{\frac{3}{2}}}{3} + \frac{2 B b x^{\frac{7}{2}}}{7} + \frac{2 x^{\frac{5}{2}} \left (A b + B a\right )}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(B*x+A)*x**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.249327, size = 39, normalized size = 1. \[ \frac{2}{7} \, B b x^{\frac{7}{2}} + \frac{2}{5} \, B a x^{\frac{5}{2}} + \frac{2}{5} \, A b x^{\frac{5}{2}} + \frac{2}{3} \, A a x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)*sqrt(x),x, algorithm="giac")
[Out]