Optimal. Leaf size=31 \[ \frac{1}{12} (2 x+3)^3 (2 d-3 e)+\frac{1}{16} e (2 x+3)^4 \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0558223, antiderivative size = 31, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ \frac{1}{12} (2 x+3)^3 (2 d-3 e)+\frac{1}{16} e (2 x+3)^4 \]
Antiderivative was successfully verified.
[In] Int[(d + e*x)*(9 + 12*x + 4*x^2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 10.234, size = 22, normalized size = 0.71 \[ \frac{e \left (2 x + 3\right )^{4}}{16} + \left (\frac{d}{6} - \frac{e}{4}\right ) \left (2 x + 3\right )^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x+d)*(4*x**2+12*x+9),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0104798, size = 36, normalized size = 1.16 \[ \frac{4}{3} x^3 (d+3 e)+\frac{3}{2} x^2 (4 d+3 e)+9 d x+e x^4 \]
Antiderivative was successfully verified.
[In] Integrate[(d + e*x)*(9 + 12*x + 4*x^2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.001, size = 35, normalized size = 1.1 \[ e{x}^{4}+{\frac{ \left ( 4\,d+12\,e \right ){x}^{3}}{3}}+{\frac{ \left ( 12\,d+9\,e \right ){x}^{2}}{2}}+9\,dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x+d)*(4*x^2+12*x+9),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.6807, size = 43, normalized size = 1.39 \[ e x^{4} + \frac{4}{3} \,{\left (d + 3 \, e\right )} x^{3} + \frac{3}{2} \,{\left (4 \, d + 3 \, e\right )} x^{2} + 9 \, d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(4*x^2 + 12*x + 9),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.179584, size = 1, normalized size = 0.03 \[ x^{4} e + 4 x^{3} e + \frac{4}{3} x^{3} d + \frac{9}{2} x^{2} e + 6 x^{2} d + 9 x d \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(4*x^2 + 12*x + 9),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.088081, size = 32, normalized size = 1.03 \[ 9 d x + e x^{4} + x^{3} \left (\frac{4 d}{3} + 4 e\right ) + x^{2} \left (6 d + \frac{9 e}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x+d)*(4*x**2+12*x+9),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.208945, size = 50, normalized size = 1.61 \[ x^{4} e + \frac{4}{3} \, d x^{3} + 4 \, x^{3} e + 6 \, d x^{2} + \frac{9}{2} \, x^{2} e + 9 \, d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(4*x^2 + 12*x + 9),x, algorithm="giac")
[Out]