Optimal. Leaf size=68 \[ -\frac{a C+A b}{4 x^4}-\frac{a A}{6 x^6}-\frac{a B}{5 x^5}-\frac{A c+b C}{2 x^2}-\frac{b B}{3 x^3}-\frac{B c}{x}+c C \log (x) \]
[Out]
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Rubi [A] time = 0.0953815, antiderivative size = 68, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.038 \[ -\frac{a C+A b}{4 x^4}-\frac{a A}{6 x^6}-\frac{a B}{5 x^5}-\frac{A c+b C}{2 x^2}-\frac{b B}{3 x^3}-\frac{B c}{x}+c C \log (x) \]
Antiderivative was successfully verified.
[In] Int[((A + B*x + C*x^2)*(a + b*x^2 + c*x^4))/x^7,x]
[Out]
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Rubi in Sympy [A] time = 18.8801, size = 63, normalized size = 0.93 \[ - \frac{A a}{6 x^{6}} - \frac{B a}{5 x^{5}} - \frac{B b}{3 x^{3}} - \frac{B c}{x} + C c \log{\left (x \right )} - \frac{\frac{A c}{2} + \frac{C b}{2}}{x^{2}} - \frac{\frac{A b}{4} + \frac{C a}{4}}{x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((C*x**2+B*x+A)*(c*x**4+b*x**2+a)/x**7,x)
[Out]
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Mathematica [A] time = 0.0944231, size = 68, normalized size = 1. \[ c C \log (x)-\frac{a (10 A+3 x (4 B+5 C x))+5 x^2 \left (3 A \left (b+2 c x^2\right )+2 x \left (2 b B+3 b C x+6 B c x^2\right )\right )}{60 x^6} \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x + C*x^2)*(a + b*x^2 + c*x^4))/x^7,x]
[Out]
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Maple [A] time = 0.009, size = 63, normalized size = 0.9 \[ -{\frac{bB}{3\,{x}^{3}}}-{\frac{Aa}{6\,{x}^{6}}}+cC\ln \left ( x \right ) -{\frac{Bc}{x}}-{\frac{Ac}{2\,{x}^{2}}}-{\frac{bC}{2\,{x}^{2}}}-{\frac{Ba}{5\,{x}^{5}}}-{\frac{Ab}{4\,{x}^{4}}}-{\frac{aC}{4\,{x}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((C*x^2+B*x+A)*(c*x^4+b*x^2+a)/x^7,x)
[Out]
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Maxima [A] time = 0.711381, size = 80, normalized size = 1.18 \[ C c \log \left (x\right ) - \frac{60 \, B c x^{5} + 20 \, B b x^{3} + 30 \,{\left (C b + A c\right )} x^{4} + 12 \, B a x + 15 \,{\left (C a + A b\right )} x^{2} + 10 \, A a}{60 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)*(C*x^2 + B*x + A)/x^7,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.247652, size = 84, normalized size = 1.24 \[ \frac{60 \, C c x^{6} \log \left (x\right ) - 60 \, B c x^{5} - 20 \, B b x^{3} - 30 \,{\left (C b + A c\right )} x^{4} - 12 \, B a x - 15 \,{\left (C a + A b\right )} x^{2} - 10 \, A a}{60 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)*(C*x^2 + B*x + A)/x^7,x, algorithm="fricas")
[Out]
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Sympy [A] time = 59.1961, size = 66, normalized size = 0.97 \[ C c \log{\left (x \right )} - \frac{10 A a + 12 B a x + 20 B b x^{3} + 60 B c x^{5} + x^{4} \left (30 A c + 30 C b\right ) + x^{2} \left (15 A b + 15 C a\right )}{60 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((C*x**2+B*x+A)*(c*x**4+b*x**2+a)/x**7,x)
[Out]
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GIAC/XCAS [A] time = 0.280958, size = 81, normalized size = 1.19 \[ C c{\rm ln}\left ({\left | x \right |}\right ) - \frac{60 \, B c x^{5} + 20 \, B b x^{3} + 30 \,{\left (C b + A c\right )} x^{4} + 12 \, B a x + 15 \,{\left (C a + A b\right )} x^{2} + 10 \, A a}{60 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)*(C*x^2 + B*x + A)/x^7,x, algorithm="giac")
[Out]