Optimal. Leaf size=47 \[ \frac{1}{3} x^3 (a e+b d)+\frac{1}{2} a d x^2+\frac{1}{4} x^4 (b e+c d)+\frac{1}{5} c e x^5 \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0928389, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{1}{3} x^3 (a e+b d)+\frac{1}{2} a d x^2+\frac{1}{4} x^4 (b e+c d)+\frac{1}{5} c e x^5 \]
Antiderivative was successfully verified.
[In] Int[x*(d + e*x)*(a + b*x + c*x^2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ a d \int x\, dx + \frac{c e x^{5}}{5} + x^{4} \left (\frac{b e}{4} + \frac{c d}{4}\right ) + x^{3} \left (\frac{a e}{3} + \frac{b d}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(e*x+d)*(c*x**2+b*x+a),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0255417, size = 41, normalized size = 0.87 \[ \frac{1}{60} x^2 \left (20 x (a e+b d)+30 a d+15 x^2 (b e+c d)+12 c e x^3\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x*(d + e*x)*(a + b*x + c*x^2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0., size = 40, normalized size = 0.9 \[{\frac{ad{x}^{2}}{2}}+{\frac{ \left ( ae+bd \right ){x}^{3}}{3}}+{\frac{ \left ( be+cd \right ){x}^{4}}{4}}+{\frac{ce{x}^{5}}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(e*x+d)*(c*x^2+b*x+a),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.699036, size = 53, normalized size = 1.13 \[ \frac{1}{5} \, c e x^{5} + \frac{1}{4} \,{\left (c d + b e\right )} x^{4} + \frac{1}{2} \, a d x^{2} + \frac{1}{3} \,{\left (b d + a e\right )} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(e*x + d)*x,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.238455, size = 1, normalized size = 0.02 \[ \frac{1}{5} x^{5} e c + \frac{1}{4} x^{4} d c + \frac{1}{4} x^{4} e b + \frac{1}{3} x^{3} d b + \frac{1}{3} x^{3} e a + \frac{1}{2} x^{2} d a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(e*x + d)*x,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.09529, size = 42, normalized size = 0.89 \[ \frac{a d x^{2}}{2} + \frac{c e x^{5}}{5} + x^{4} \left (\frac{b e}{4} + \frac{c d}{4}\right ) + x^{3} \left (\frac{a e}{3} + \frac{b d}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(e*x+d)*(c*x**2+b*x+a),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.309471, size = 62, normalized size = 1.32 \[ \frac{1}{5} \, c x^{5} e + \frac{1}{4} \, c d x^{4} + \frac{1}{4} \, b x^{4} e + \frac{1}{3} \, b d x^{3} + \frac{1}{3} \, a x^{3} e + \frac{1}{2} \, a d x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(e*x + d)*x,x, algorithm="giac")
[Out]