Optimal. Leaf size=32 \[ \frac{1}{3} e^{3 x} x^2-\frac{2}{9} e^{3 x} x+\frac{2 e^{3 x}}{27} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0322933, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ \frac{1}{3} e^{3 x} x^2-\frac{2}{9} e^{3 x} x+\frac{2 e^{3 x}}{27} \]
Antiderivative was successfully verified.
[In] Int[E^(3*x)*x^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.15312, size = 27, normalized size = 0.84 \[ \frac{x^{2} e^{3 x}}{3} - \frac{2 x e^{3 x}}{9} + \frac{2 e^{3 x}}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(3*x)*x**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00356269, size = 19, normalized size = 0.59 \[ \frac{1}{27} e^{3 x} \left (9 x^2-6 x+2\right ) \]
Antiderivative was successfully verified.
[In] Integrate[E^(3*x)*x^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.005, size = 17, normalized size = 0.5 \[{\frac{ \left ( 9\,{x}^{2}-6\,x+2 \right ){{\rm e}^{3\,x}}}{27}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(3*x)*x^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.35018, size = 22, normalized size = 0.69 \[ \frac{1}{27} \,{\left (9 \, x^{2} - 6 \, x + 2\right )} e^{\left (3 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2*e^(3*x),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.198966, size = 22, normalized size = 0.69 \[ \frac{1}{27} \,{\left (9 \, x^{2} - 6 \, x + 2\right )} e^{\left (3 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2*e^(3*x),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.085207, size = 15, normalized size = 0.47 \[ \frac{\left (9 x^{2} - 6 x + 2\right ) e^{3 x}}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(3*x)*x**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.208055, size = 22, normalized size = 0.69 \[ \frac{1}{27} \,{\left (9 \, x^{2} - 6 \, x + 2\right )} e^{\left (3 \, x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2*e^(3*x),x, algorithm="giac")
[Out]