Optimal. Leaf size=39 \[ \frac{2}{5} x^{5/2} (A c+b B)+\frac{2}{3} A b x^{3/2}+\frac{2}{7} B c x^{7/2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0495241, antiderivative size = 39, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ \frac{2}{5} x^{5/2} (A c+b B)+\frac{2}{3} A b x^{3/2}+\frac{2}{7} B c x^{7/2} \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(b*x + c*x^2))/Sqrt[x],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 6.35299, size = 41, normalized size = 1.05 \[ \frac{2 A b x^{\frac{3}{2}}}{3} + \frac{2 B c x^{\frac{7}{2}}}{7} + x^{\frac{5}{2}} \left (\frac{2 A c}{5} + \frac{2 B b}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(c*x**2+b*x)/x**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0186771, size = 33, normalized size = 0.85 \[ \frac{2}{105} x^{3/2} (7 A (5 b+3 c x)+3 B x (7 b+5 c x)) \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(b*x + c*x^2))/Sqrt[x],x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.005, size = 28, normalized size = 0.7 \[{\frac{30\,Bc{x}^{2}+42\,Acx+42\,xBb+70\,Ab}{105}{x}^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(c*x^2+b*x)/x^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.676853, size = 36, normalized size = 0.92 \[ \frac{2}{7} \, B c x^{\frac{7}{2}} + \frac{2}{3} \, A b x^{\frac{3}{2}} + \frac{2}{5} \,{\left (B b + A c\right )} x^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)*(B*x + A)/sqrt(x),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.289262, size = 41, normalized size = 1.05 \[ \frac{2}{105} \,{\left (15 \, B c x^{3} + 35 \, A b x + 21 \,{\left (B b + A c\right )} x^{2}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)*(B*x + A)/sqrt(x),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 2.47101, size = 46, normalized size = 1.18 \[ \frac{2 A b x^{\frac{3}{2}}}{3} + \frac{2 A c x^{\frac{5}{2}}}{5} + \frac{2 B b x^{\frac{5}{2}}}{5} + \frac{2 B c x^{\frac{7}{2}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(c*x**2+b*x)/x**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.265616, size = 39, normalized size = 1. \[ \frac{2}{7} \, B c x^{\frac{7}{2}} + \frac{2}{5} \, B b x^{\frac{5}{2}} + \frac{2}{5} \, A c x^{\frac{5}{2}} + \frac{2}{3} \, A b x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)*(B*x + A)/sqrt(x),x, algorithm="giac")
[Out]