Optimal. Leaf size=45 \[ \frac{2}{3} a A x^{3/2}+\frac{2}{5} a B x^{5/2}+\frac{2}{7} A c x^{7/2}+\frac{2}{9} B c x^{9/2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0386267, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ \frac{2}{3} a A x^{3/2}+\frac{2}{5} a B x^{5/2}+\frac{2}{7} A c x^{7/2}+\frac{2}{9} B c x^{9/2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[x]*(A + B*x)*(a + c*x^2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.02973, size = 46, normalized size = 1.02 \[ \frac{2 A a x^{\frac{3}{2}}}{3} + \frac{2 A c x^{\frac{7}{2}}}{7} + \frac{2 B a x^{\frac{5}{2}}}{5} + \frac{2 B c x^{\frac{9}{2}}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(c*x**2+a)*x**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0191145, size = 35, normalized size = 0.78 \[ \frac{2}{315} x^{3/2} \left (21 a (5 A+3 B x)+5 c x^2 (9 A+7 B x)\right ) \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[x]*(A + B*x)*(a + c*x^2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.005, size = 30, normalized size = 0.7 \[{\frac{70\,Bc{x}^{3}+90\,Ac{x}^{2}+126\,aBx+210\,aA}{315}{x}^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(c*x^2+a)*x^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.684977, size = 39, normalized size = 0.87 \[ \frac{2}{9} \, B c x^{\frac{9}{2}} + \frac{2}{7} \, A c x^{\frac{7}{2}} + \frac{2}{5} \, B a x^{\frac{5}{2}} + \frac{2}{3} \, A a x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)*(B*x + A)*sqrt(x),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.276821, size = 43, normalized size = 0.96 \[ \frac{2}{315} \,{\left (35 \, B c x^{4} + 45 \, A c x^{3} + 63 \, B a x^{2} + 105 \, A a x\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)*(B*x + A)*sqrt(x),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 2.52079, size = 46, normalized size = 1.02 \[ \frac{2 A a x^{\frac{3}{2}}}{3} + \frac{2 A c x^{\frac{7}{2}}}{7} + \frac{2 B a x^{\frac{5}{2}}}{5} + \frac{2 B c x^{\frac{9}{2}}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(c*x**2+a)*x**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.268115, size = 39, normalized size = 0.87 \[ \frac{2}{9} \, B c x^{\frac{9}{2}} + \frac{2}{7} \, A c x^{\frac{7}{2}} + \frac{2}{5} \, B a x^{\frac{5}{2}} + \frac{2}{3} \, A a x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)*(B*x + A)*sqrt(x),x, algorithm="giac")
[Out]