Optimal. Leaf size=42 \[ \frac{1}{28} \left (4 x^2+12 x+9\right )^{7/2}-\frac{1}{8} (2 x+3) \left (4 x^2+12 x+9\right )^{5/2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0325436, antiderivative size = 42, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ \frac{1}{28} \left (4 x^2+12 x+9\right )^{7/2}-\frac{1}{8} (2 x+3) \left (4 x^2+12 x+9\right )^{5/2} \]
Antiderivative was successfully verified.
[In] Int[x*(9 + 12*x + 4*x^2)^(5/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 3.83275, size = 34, normalized size = 0.81 \[ - \frac{\left (8 x + 12\right ) \left (4 x^{2} + 12 x + 9\right )^{\frac{5}{2}}}{32} + \frac{\left (4 x^{2} + 12 x + 9\right )^{\frac{7}{2}}}{28} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(4*x**2+12*x+9)**(5/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0263512, size = 47, normalized size = 1.12 \[ \frac{x^2 \sqrt{(2 x+3)^2} \left (64 x^5+560 x^4+2016 x^3+3780 x^2+3780 x+1701\right )}{28 x+42} \]
Antiderivative was successfully verified.
[In] Integrate[x*(9 + 12*x + 4*x^2)^(5/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.005, size = 47, normalized size = 1.1 \[{\frac{{x}^{2} \left ( 64\,{x}^{5}+560\,{x}^{4}+2016\,{x}^{3}+3780\,{x}^{2}+3780\,x+1701 \right ) }{14\, \left ( 2\,x+3 \right ) ^{5}} \left ( \left ( 2\,x+3 \right ) ^{2} \right ) ^{{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(4*x^2+12*x+9)^(5/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.883183, size = 59, normalized size = 1.4 \[ \frac{1}{28} \,{\left (4 \, x^{2} + 12 \, x + 9\right )}^{\frac{7}{2}} - \frac{1}{4} \,{\left (4 \, x^{2} + 12 \, x + 9\right )}^{\frac{5}{2}} x - \frac{3}{8} \,{\left (4 \, x^{2} + 12 \, x + 9\right )}^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x^2 + 12*x + 9)^(5/2)*x,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.215693, size = 42, normalized size = 1. \[ \frac{32}{7} \, x^{7} + 40 \, x^{6} + 144 \, x^{5} + 270 \, x^{4} + 270 \, x^{3} + \frac{243}{2} \, x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x^2 + 12*x + 9)^(5/2)*x,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int x \left (\left (2 x + 3\right )^{2}\right )^{\frac{5}{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(4*x**2+12*x+9)**(5/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.20779, size = 101, normalized size = 2.4 \[ \frac{32}{7} \, x^{7}{\rm sign}\left (2 \, x + 3\right ) + 40 \, x^{6}{\rm sign}\left (2 \, x + 3\right ) + 144 \, x^{5}{\rm sign}\left (2 \, x + 3\right ) + 270 \, x^{4}{\rm sign}\left (2 \, x + 3\right ) + 270 \, x^{3}{\rm sign}\left (2 \, x + 3\right ) + \frac{243}{2} \, x^{2}{\rm sign}\left (2 \, x + 3\right ) - \frac{729}{56} \,{\rm sign}\left (2 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x^2 + 12*x + 9)^(5/2)*x,x, algorithm="giac")
[Out]