Optimal. Leaf size=112 \[ \frac{1}{4} x^4 (a d f h+b (c f h+d e h+d f g))+\frac{1}{3} x^3 (a (c f h+d e h+d f g)+b (c e h+c f g+d e g))+\frac{1}{2} x^2 (a (c e h+c f g+d e g)+b c e g)+a c e g x+\frac{1}{5} b d f h x^5 \]
[Out]
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Rubi [A] time = 0.413653, antiderivative size = 112, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048 \[ \frac{1}{4} x^4 (a d f h+b (c f h+d e h+d f g))+\frac{1}{3} x^3 (a (c f h+d e h+d f g)+b (c e h+c f g+d e g))+\frac{1}{2} x^2 (a (c e h+c f g+d e g)+b c e g)+a c e g x+\frac{1}{5} b d f h x^5 \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)*(c + d*x)*(e + f*x)*(g + h*x),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{b d f h x^{5}}{5} + c e g \int a\, dx + x^{4} \left (\frac{a d f h}{4} + \frac{b c f h}{4} + \frac{b d e h}{4} + \frac{b d f g}{4}\right ) + x^{3} \left (\frac{a c f h}{3} + \frac{a d e h}{3} + \frac{a d f g}{3} + \frac{b c e h}{3} + \frac{b c f g}{3} + \frac{b d e g}{3}\right ) + \left (a c e h + a c f g + a d e g + b c e g\right ) \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(d*x+c)*(f*x+e)*(h*x+g),x)
[Out]
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Mathematica [A] time = 0.0899341, size = 112, normalized size = 1. \[ \frac{1}{4} x^4 (a d f h+b c f h+b d e h+b d f g)+\frac{1}{3} x^3 (a c f h+a d e h+a d f g+b c e h+b c f g+b d e g)+\frac{1}{2} x^2 (a c e h+a c f g+a d e g+b c e g)+a c e g x+\frac{1}{5} b d f h x^5 \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)*(c + d*x)*(e + f*x)*(g + h*x),x]
[Out]
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Maple [A] time = 0.008, size = 109, normalized size = 1. \[{\frac{bdfh{x}^{5}}{5}}+{\frac{ \left ( \left ( \left ( ad+bc \right ) f+bde \right ) h+bdfg \right ){x}^{4}}{4}}+{\frac{ \left ( \left ( acf+ \left ( ad+bc \right ) e \right ) h+ \left ( \left ( ad+bc \right ) f+bde \right ) g \right ){x}^{3}}{3}}+{\frac{ \left ( aceh+ \left ( acf+ \left ( ad+bc \right ) e \right ) g \right ){x}^{2}}{2}}+acegx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(d*x+c)*(f*x+e)*(h*x+g),x)
[Out]
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Maxima [A] time = 1.36309, size = 146, normalized size = 1.3 \[ \frac{1}{5} \, b d f h x^{5} + a c e g x + \frac{1}{4} \,{\left (b d f g +{\left (b d e +{\left (b c + a d\right )} f\right )} h\right )} x^{4} + \frac{1}{3} \,{\left ({\left (b d e +{\left (b c + a d\right )} f\right )} g +{\left (a c f +{\left (b c + a d\right )} e\right )} h\right )} x^{3} + \frac{1}{2} \,{\left (a c e h +{\left (a c f +{\left (b c + a d\right )} e\right )} g\right )} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*(d*x + c)*(f*x + e)*(h*x + g),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.18605, size = 1, normalized size = 0.01 \[ \frac{1}{5} x^{5} h f d b + \frac{1}{4} x^{4} g f d b + \frac{1}{4} x^{4} h e d b + \frac{1}{4} x^{4} h f c b + \frac{1}{4} x^{4} h f d a + \frac{1}{3} x^{3} g e d b + \frac{1}{3} x^{3} g f c b + \frac{1}{3} x^{3} h e c b + \frac{1}{3} x^{3} g f d a + \frac{1}{3} x^{3} h e d a + \frac{1}{3} x^{3} h f c a + \frac{1}{2} x^{2} g e c b + \frac{1}{2} x^{2} g e d a + \frac{1}{2} x^{2} g f c a + \frac{1}{2} x^{2} h e c a + x g e c a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*(d*x + c)*(f*x + e)*(h*x + g),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.152948, size = 148, normalized size = 1.32 \[ a c e g x + \frac{b d f h x^{5}}{5} + x^{4} \left (\frac{a d f h}{4} + \frac{b c f h}{4} + \frac{b d e h}{4} + \frac{b d f g}{4}\right ) + x^{3} \left (\frac{a c f h}{3} + \frac{a d e h}{3} + \frac{a d f g}{3} + \frac{b c e h}{3} + \frac{b c f g}{3} + \frac{b d e g}{3}\right ) + x^{2} \left (\frac{a c e h}{2} + \frac{a c f g}{2} + \frac{a d e g}{2} + \frac{b c e g}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(d*x+c)*(f*x+e)*(h*x+g),x)
[Out]
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GIAC/XCAS [A] time = 0.209786, size = 203, normalized size = 1.81 \[ \frac{1}{5} \, b d f h x^{5} + \frac{1}{4} \, b d f g x^{4} + \frac{1}{4} \, b c f h x^{4} + \frac{1}{4} \, a d f h x^{4} + \frac{1}{4} \, b d h x^{4} e + \frac{1}{3} \, b c f g x^{3} + \frac{1}{3} \, a d f g x^{3} + \frac{1}{3} \, a c f h x^{3} + \frac{1}{3} \, b d g x^{3} e + \frac{1}{3} \, b c h x^{3} e + \frac{1}{3} \, a d h x^{3} e + \frac{1}{2} \, a c f g x^{2} + \frac{1}{2} \, b c g x^{2} e + \frac{1}{2} \, a d g x^{2} e + \frac{1}{2} \, a c h x^{2} e + a c g x e \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*(d*x + c)*(f*x + e)*(h*x + g),x, algorithm="giac")
[Out]