Optimal. Leaf size=99 \[ -\frac{a^2 A}{6 x^6}-\frac{A \left (2 a c+b^2\right )+2 a b B}{4 x^4}-\frac{2 a B c+2 A b c+b^2 B}{3 x^3}-\frac{a (a B+2 A b)}{5 x^5}-\frac{c (A c+2 b B)}{2 x^2}-\frac{B c^2}{x} \]
[Out]
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Rubi [A] time = 0.143587, antiderivative size = 99, 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 \[ -\frac{a^2 A}{6 x^6}-\frac{A \left (2 a c+b^2\right )+2 a b B}{4 x^4}-\frac{2 a B c+2 A b c+b^2 B}{3 x^3}-\frac{a (a B+2 A b)}{5 x^5}-\frac{c (A c+2 b B)}{2 x^2}-\frac{B c^2}{x} \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(a + b*x + c*x^2)^2)/x^7,x]
[Out]
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Rubi in Sympy [A] time = 22.6189, size = 99, normalized size = 1. \[ - \frac{A a^{2}}{6 x^{6}} - \frac{B c^{2}}{x} - \frac{a \left (2 A b + B a\right )}{5 x^{5}} - \frac{c \left (A c + 2 B b\right )}{2 x^{2}} - \frac{\frac{2 A b c}{3} + \frac{2 B a c}{3} + \frac{B b^{2}}{3}}{x^{3}} - \frac{\frac{A a c}{2} + \frac{A b^{2}}{4} + \frac{B a b}{2}}{x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(c*x**2+b*x+a)**2/x**7,x)
[Out]
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Mathematica [A] time = 0.0783942, size = 97, normalized size = 0.98 \[ -\frac{2 a^2 (5 A+6 B x)+2 a x (3 A (4 b+5 c x)+5 B x (3 b+4 c x))+5 x^2 \left (A \left (3 b^2+8 b c x+6 c^2 x^2\right )+4 B x \left (b^2+3 b c x+3 c^2 x^2\right )\right )}{60 x^6} \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(a + b*x + c*x^2)^2)/x^7,x]
[Out]
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Maple [A] time = 0.007, size = 90, normalized size = 0.9 \[ -{\frac{A{a}^{2}}{6\,{x}^{6}}}-{\frac{2\,aAc+{b}^{2}A+2\,abB}{4\,{x}^{4}}}-{\frac{2\,Abc+2\,aBc+{b}^{2}B}{3\,{x}^{3}}}-{\frac{c \left ( Ac+2\,Bb \right ) }{2\,{x}^{2}}}-{\frac{a \left ( 2\,Ab+Ba \right ) }{5\,{x}^{5}}}-{\frac{B{c}^{2}}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(c*x^2+b*x+a)^2/x^7,x)
[Out]
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Maxima [A] time = 0.6923, size = 126, normalized size = 1.27 \[ -\frac{60 \, B c^{2} x^{5} + 30 \,{\left (2 \, B b c + A c^{2}\right )} x^{4} + 20 \,{\left (B b^{2} + 2 \,{\left (B a + A b\right )} c\right )} x^{3} + 10 \, A a^{2} + 15 \,{\left (2 \, B a b + A b^{2} + 2 \, A a c\right )} x^{2} + 12 \,{\left (B a^{2} + 2 \, A a b\right )} x}{60 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)^2*(B*x + A)/x^7,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.264776, size = 126, normalized size = 1.27 \[ -\frac{60 \, B c^{2} x^{5} + 30 \,{\left (2 \, B b c + A c^{2}\right )} x^{4} + 20 \,{\left (B b^{2} + 2 \,{\left (B a + A b\right )} c\right )} x^{3} + 10 \, A a^{2} + 15 \,{\left (2 \, B a b + A b^{2} + 2 \, A a c\right )} x^{2} + 12 \,{\left (B a^{2} + 2 \, A a b\right )} x}{60 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)^2*(B*x + A)/x^7,x, algorithm="fricas")
[Out]
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Sympy [A] time = 50.1274, size = 102, normalized size = 1.03 \[ - \frac{10 A a^{2} + 60 B c^{2} x^{5} + x^{4} \left (30 A c^{2} + 60 B b c\right ) + x^{3} \left (40 A b c + 40 B a c + 20 B b^{2}\right ) + x^{2} \left (30 A a c + 15 A b^{2} + 30 B a b\right ) + x \left (24 A a b + 12 B a^{2}\right )}{60 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(c*x**2+b*x+a)**2/x**7,x)
[Out]
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GIAC/XCAS [A] time = 0.267763, size = 136, normalized size = 1.37 \[ -\frac{60 \, B c^{2} x^{5} + 60 \, B b c x^{4} + 30 \, A c^{2} x^{4} + 20 \, B b^{2} x^{3} + 40 \, B a c x^{3} + 40 \, A b c x^{3} + 30 \, B a b x^{2} + 15 \, A b^{2} x^{2} + 30 \, A a c x^{2} + 12 \, B a^{2} x + 24 \, A a b x + 10 \, A a^{2}}{60 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)^2*(B*x + A)/x^7,x, algorithm="giac")
[Out]