Optimal. Leaf size=63 \[ \log (x) (a C+A b)-\frac{a A}{2 x^2}-\frac{a B}{x}+\frac{1}{2} x^2 (A c+b C)+b B x+\frac{1}{3} B c x^3+\frac{1}{4} c C x^4 \]
[Out]
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Rubi [A] time = 0.100985, antiderivative size = 63, 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 \[ \log (x) (a C+A b)-\frac{a A}{2 x^2}-\frac{a B}{x}+\frac{1}{2} x^2 (A c+b C)+b B x+\frac{1}{3} B c x^3+\frac{1}{4} c C x^4 \]
Antiderivative was successfully verified.
[In] Int[((A + B*x + C*x^2)*(a + b*x^2 + c*x^4))/x^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{A a}{2 x^{2}} - \frac{B a}{x} + \frac{B c x^{3}}{3} + \frac{C c x^{4}}{4} + b \int B\, dx + \left (A b + C a\right ) \log{\left (x \right )} + \left (A c + C b\right ) \int x\, dx \]
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**3,x)
[Out]
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Mathematica [A] time = 0.075531, size = 58, normalized size = 0.92 \[ \log (x) (a C+A b)-\frac{a (A+2 B x)}{2 x^2}+\frac{1}{12} x \left (c x \left (6 A+4 B x+3 C x^2\right )+6 b (2 B+C x)\right ) \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x + C*x^2)*(a + b*x^2 + c*x^4))/x^3,x]
[Out]
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Maple [A] time = 0.008, size = 58, normalized size = 0.9 \[{\frac{cC{x}^{4}}{4}}+{\frac{Bc{x}^{3}}{3}}+{\frac{Ac{x}^{2}}{2}}+{\frac{C{x}^{2}b}{2}}+bBx+A\ln \left ( x \right ) b+C\ln \left ( x \right ) a-{\frac{Ba}{x}}-{\frac{Aa}{2\,{x}^{2}}} \]
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^3,x)
[Out]
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Maxima [A] time = 0.712012, size = 74, normalized size = 1.17 \[ \frac{1}{4} \, C c x^{4} + \frac{1}{3} \, B c x^{3} + B b x + \frac{1}{2} \,{\left (C b + A c\right )} x^{2} +{\left (C a + A b\right )} \log \left (x\right ) - \frac{2 \, B a x + A a}{2 \, x^{2}} \]
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^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.248793, size = 84, normalized size = 1.33 \[ \frac{3 \, C c x^{6} + 4 \, B c x^{5} + 12 \, B b x^{3} + 6 \,{\left (C b + A c\right )} x^{4} + 12 \,{\left (C a + A b\right )} x^{2} \log \left (x\right ) - 12 \, B a x - 6 \, A a}{12 \, x^{2}} \]
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^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.70048, size = 60, normalized size = 0.95 \[ B b x + \frac{B c x^{3}}{3} + \frac{C c x^{4}}{4} + x^{2} \left (\frac{A c}{2} + \frac{C b}{2}\right ) + \left (A b + C a\right ) \log{\left (x \right )} - \frac{A a + 2 B a x}{2 x^{2}} \]
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**3,x)
[Out]
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GIAC/XCAS [A] time = 0.280595, size = 78, normalized size = 1.24 \[ \frac{1}{4} \, C c x^{4} + \frac{1}{3} \, B c x^{3} + \frac{1}{2} \, C b x^{2} + \frac{1}{2} \, A c x^{2} + B b x +{\left (C a + A b\right )}{\rm ln}\left ({\left | x \right |}\right ) - \frac{2 \, B a x + A a}{2 \, x^{2}} \]
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^3,x, algorithm="giac")
[Out]