Optimal. Leaf size=56 \[ \frac{1}{3} x^3 (a d f+b c f+b d e)+\frac{1}{2} x^2 (a c f+a d e+b c e)+a c e x+\frac{1}{4} b d f x^4 \]
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Rubi [A] time = 0.0455521, antiderivative size = 56, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 44, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \frac{1}{3} x^3 (a d f+b c f+b d e)+\frac{1}{2} x^2 (a c f+a d e+b c e)+a c e x+\frac{1}{4} b d f x^4 \]
Antiderivative was successfully verified.
[In] Int[a*c*e + (b*c*e + a*d*e + a*c*f)*x + (b*d*e + b*c*f + a*d*f)*x^2 + b*d*f*x^3,x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{b d f x^{4}}{4} + c e \int a\, dx + x^{3} \left (\frac{a d f}{3} + \frac{b c f}{3} + \frac{b d e}{3}\right ) + \left (a c f + a d e + b c e\right ) \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x**2+b*d*f*x**3,x)
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Mathematica [A] time = 0.0000892753, size = 76, normalized size = 1.36 \[ a c e x+\frac{1}{2} a c f x^2+\frac{1}{2} a d e x^2+\frac{1}{3} a d f x^3+\frac{1}{2} b c e x^2+\frac{1}{3} b c f x^3+\frac{1}{3} b d e x^3+\frac{1}{4} b d f x^4 \]
Antiderivative was successfully verified.
[In] Integrate[a*c*e + (b*c*e + a*d*e + a*c*f)*x + (b*d*e + b*c*f + a*d*f)*x^2 + b*d*f*x^3,x]
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Maple [A] time = 0.001, size = 51, normalized size = 0.9 \[ acex+{\frac{ \left ( acf+ade+bce \right ){x}^{2}}{2}}+{\frac{ \left ( adf+bcf+bde \right ){x}^{3}}{3}}+{\frac{bdf{x}^{4}}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3,x)
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Maxima [A] time = 0.76833, size = 68, normalized size = 1.21 \[ \frac{1}{4} \, b d f x^{4} + a c e x + \frac{1}{3} \,{\left (b d e + b c f + a d f\right )} x^{3} + \frac{1}{2} \,{\left (b c e + a d e + a c f\right )} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(b*d*f*x^3 + a*c*e + (b*d*e + b*c*f + a*d*f)*x^2 + (b*c*e + a*d*e + a*c*f)*x,x, algorithm="maxima")
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Fricas [A] time = 0.278045, size = 1, normalized size = 0.02 \[ \frac{1}{4} x^{4} f d b + \frac{1}{3} x^{3} e d b + \frac{1}{3} x^{3} f c b + \frac{1}{3} x^{3} f d a + \frac{1}{2} x^{2} e c b + \frac{1}{2} x^{2} e d a + \frac{1}{2} x^{2} f c a + x e c a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(b*d*f*x^3 + a*c*e + (b*d*e + b*c*f + a*d*f)*x^2 + (b*c*e + a*d*e + a*c*f)*x,x, algorithm="fricas")
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Sympy [A] time = 0.109789, size = 63, normalized size = 1.12 \[ a c e x + \frac{b d f x^{4}}{4} + x^{3} \left (\frac{a d f}{3} + \frac{b c f}{3} + \frac{b d e}{3}\right ) + x^{2} \left (\frac{a c f}{2} + \frac{a d e}{2} + \frac{b c e}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x**2+b*d*f*x**3,x)
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GIAC/XCAS [A] time = 0.262889, size = 73, normalized size = 1.3 \[ \frac{1}{4} \, b d f x^{4} + \frac{1}{3} \,{\left (b c f + a d f + b d e\right )} x^{3} + a c x e + \frac{1}{2} \,{\left (a c f + b c e + a d e\right )} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(b*d*f*x^3 + a*c*e + (b*d*e + b*c*f + a*d*f)*x^2 + (b*c*e + a*d*e + a*c*f)*x,x, algorithm="giac")
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