Optimal. Leaf size=31 \[ \frac{e \left (a+c x^2\right )^2}{4 c}+a d x+\frac{1}{3} c d x^3 \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0280731, antiderivative size = 31, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{e \left (a+c x^2\right )^2}{4 c}+a d x+\frac{1}{3} c d x^3 \]
Antiderivative was successfully verified.
[In] Int[(d + e*x)*(a + c*x^2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ a e \int x\, dx + \frac{c d x^{3}}{3} + \frac{c e x^{4}}{4} + d \int a\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x+d)*(c*x**2+a),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00287985, size = 32, normalized size = 1.03 \[ a d x+\frac{1}{2} a e x^2+\frac{1}{3} c d x^3+\frac{1}{4} c e x^4 \]
Antiderivative was successfully verified.
[In] Integrate[(d + e*x)*(a + c*x^2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.001, size = 27, normalized size = 0.9 \[{\frac{ce{x}^{4}}{4}}+{\frac{cd{x}^{3}}{3}}+{\frac{ae{x}^{2}}{2}}+adx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x+d)*(c*x^2+a),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.717783, size = 35, normalized size = 1.13 \[ \frac{1}{4} \, c e x^{4} + \frac{1}{3} \, c d x^{3} + \frac{1}{2} \, a e x^{2} + a d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)*(e*x + d),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.18282, size = 1, normalized size = 0.03 \[ \frac{1}{4} x^{4} e c + \frac{1}{3} x^{3} d c + \frac{1}{2} x^{2} e a + x d a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)*(e*x + d),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.079065, size = 29, normalized size = 0.94 \[ a d x + \frac{a e x^{2}}{2} + \frac{c d x^{3}}{3} + \frac{c e x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x+d)*(c*x**2+a),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.203953, size = 38, normalized size = 1.23 \[ \frac{1}{4} \, c x^{4} e + \frac{1}{3} \, c d x^{3} + \frac{1}{2} \, a x^{2} e + a d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)*(e*x + d),x, algorithm="giac")
[Out]