Optimal. Leaf size=56 \[ \frac{1}{3} x^3 (a d f+b c f+b d e)+\frac{1}{2} x^2 (a c f+a d e+b c e)+a c e x+\frac{1}{4} b d f x^4 \]
[Out]
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Rubi [A] time = 0.0998885, antiderivative size = 56, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ \frac{1}{3} x^3 (a d f+b c f+b d e)+\frac{1}{2} x^2 (a c f+a d e+b c e)+a c e x+\frac{1}{4} b d f x^4 \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)*(c + d*x)*(e + f*x),x]
[Out]
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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((b*x+a)*(d*x+c)*(f*x+e),x)
[Out]
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Mathematica [A] time = 0.0336197, size = 53, normalized size = 0.95 \[ \frac{1}{12} x \left (4 x^2 (a d f+b c f+b d e)+6 x (a c f+a d e+b c e)+12 a c e+3 b d f x^3\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)*(c + d*x)*(e + f*x),x]
[Out]
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Maple [A] time = 0.001, size = 53, normalized size = 1. \[{\frac{bdf{x}^{4}}{4}}+{\frac{ \left ( \left ( ad+bc \right ) f+bde \right ){x}^{3}}{3}}+{\frac{ \left ( acf+ \left ( ad+bc \right ) e \right ){x}^{2}}{2}}+acex \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(d*x+c)*(f*x+e),x)
[Out]
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Maxima [A] time = 1.38652, size = 70, normalized size = 1.25 \[ \frac{1}{4} \, b d f x^{4} + a c e x + \frac{1}{3} \,{\left (b d e +{\left (b c + a d\right )} f\right )} x^{3} + \frac{1}{2} \,{\left (a c f +{\left (b c + a d\right )} e\right )} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*(d*x + c)*(f*x + e),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.19059, 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*x + a)*(d*x + c)*(f*x + e),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.109698, 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((b*x+a)*(d*x+c)*(f*x+e),x)
[Out]
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GIAC/XCAS [A] time = 0.209837, size = 89, normalized size = 1.59 \[ \frac{1}{4} \, b d f x^{4} + \frac{1}{3} \, b c f x^{3} + \frac{1}{3} \, a d f x^{3} + \frac{1}{3} \, b d x^{3} e + \frac{1}{2} \, a c f x^{2} + \frac{1}{2} \, b c x^{2} e + \frac{1}{2} \, a d x^{2} e + a c x e \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*(d*x + c)*(f*x + e),x, algorithm="giac")
[Out]