Optimal. Leaf size=75 \[ -\frac{A b^3}{7 x^7}-\frac{b^2 (3 A c+b B)}{6 x^6}-\frac{c^2 (A c+3 b B)}{4 x^4}-\frac{3 b c (A c+b B)}{5 x^5}-\frac{B c^3}{3 x^3} \]
[Out]
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Rubi [A] time = 0.109512, antiderivative size = 75, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ -\frac{A b^3}{7 x^7}-\frac{b^2 (3 A c+b B)}{6 x^6}-\frac{c^2 (A c+3 b B)}{4 x^4}-\frac{3 b c (A c+b B)}{5 x^5}-\frac{B c^3}{3 x^3} \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(b*x + c*x^2)^3)/x^11,x]
[Out]
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Rubi in Sympy [A] time = 15.1682, size = 71, normalized size = 0.95 \[ - \frac{A b^{3}}{7 x^{7}} - \frac{B c^{3}}{3 x^{3}} - \frac{b^{2} \left (3 A c + B b\right )}{6 x^{6}} - \frac{3 b c \left (A c + B b\right )}{5 x^{5}} - \frac{c^{2} \left (A c + 3 B b\right )}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(c*x**2+b*x)**3/x**11,x)
[Out]
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Mathematica [A] time = 0.0395493, size = 75, normalized size = 1. \[ -\frac{3 A \left (20 b^3+70 b^2 c x+84 b c^2 x^2+35 c^3 x^3\right )+7 B x \left (10 b^3+36 b^2 c x+45 b c^2 x^2+20 c^3 x^3\right )}{420 x^7} \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(b*x + c*x^2)^3)/x^11,x]
[Out]
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Maple [A] time = 0.006, size = 66, normalized size = 0.9 \[ -{\frac{A{b}^{3}}{7\,{x}^{7}}}-{\frac{{b}^{2} \left ( 3\,Ac+Bb \right ) }{6\,{x}^{6}}}-{\frac{3\,bc \left ( Ac+Bb \right ) }{5\,{x}^{5}}}-{\frac{{c}^{2} \left ( Ac+3\,Bb \right ) }{4\,{x}^{4}}}-{\frac{B{c}^{3}}{3\,{x}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(c*x^2+b*x)^3/x^11,x)
[Out]
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Maxima [A] time = 0.703882, size = 99, normalized size = 1.32 \[ -\frac{140 \, B c^{3} x^{4} + 60 \, A b^{3} + 105 \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{3} + 252 \,{\left (B b^{2} c + A b c^{2}\right )} x^{2} + 70 \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x}{420 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)/x^11,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.279149, size = 99, normalized size = 1.32 \[ -\frac{140 \, B c^{3} x^{4} + 60 \, A b^{3} + 105 \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{3} + 252 \,{\left (B b^{2} c + A b c^{2}\right )} x^{2} + 70 \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x}{420 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)/x^11,x, algorithm="fricas")
[Out]
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Sympy [A] time = 8.61083, size = 78, normalized size = 1.04 \[ - \frac{60 A b^{3} + 140 B c^{3} x^{4} + x^{3} \left (105 A c^{3} + 315 B b c^{2}\right ) + x^{2} \left (252 A b c^{2} + 252 B b^{2} c\right ) + x \left (210 A b^{2} c + 70 B b^{3}\right )}{420 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(c*x**2+b*x)**3/x**11,x)
[Out]
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GIAC/XCAS [A] time = 0.267453, size = 101, normalized size = 1.35 \[ -\frac{140 \, B c^{3} x^{4} + 315 \, B b c^{2} x^{3} + 105 \, A c^{3} x^{3} + 252 \, B b^{2} c x^{2} + 252 \, A b c^{2} x^{2} + 70 \, B b^{3} x + 210 \, A b^{2} c x + 60 \, A b^{3}}{420 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)/x^11,x, algorithm="giac")
[Out]