Optimal. Leaf size=41 \[ -\frac{a B+A b}{2 x^2}-\frac{a A}{3 x^3}-\frac{A c+b B}{x}+B c \log (x) \]
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Rubi [A] time = 0.0624709, antiderivative size = 41, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053 \[ -\frac{a B+A b}{2 x^2}-\frac{a A}{3 x^3}-\frac{A c+b B}{x}+B c \log (x) \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(a + b*x + c*x^2))/x^4,x]
[Out]
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Rubi in Sympy [A] time = 9.59198, size = 36, normalized size = 0.88 \[ - \frac{A a}{3 x^{3}} + B c \log{\left (x \right )} - \frac{A c + B b}{x} - \frac{\frac{A b}{2} + \frac{B a}{2}}{x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(c*x**2+b*x+a)/x**4,x)
[Out]
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Mathematica [A] time = 0.0506744, size = 41, normalized size = 1. \[ B c \log (x)-\frac{a (2 A+3 B x)+3 x (A b+2 A c x+2 b B x)}{6 x^3} \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(a + b*x + c*x^2))/x^4,x]
[Out]
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Maple [A] time = 0.008, size = 42, normalized size = 1. \[ Bc\ln \left ( x \right ) -{\frac{aA}{3\,{x}^{3}}}-{\frac{Ab}{2\,{x}^{2}}}-{\frac{Ba}{2\,{x}^{2}}}-{\frac{Ac}{x}}-{\frac{Bb}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(c*x^2+b*x+a)/x^4,x)
[Out]
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Maxima [A] time = 0.694569, size = 51, normalized size = 1.24 \[ B c \log \left (x\right ) - \frac{6 \,{\left (B b + A c\right )} x^{2} + 2 \, A a + 3 \,{\left (B a + A b\right )} x}{6 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A)/x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.309532, size = 55, normalized size = 1.34 \[ \frac{6 \, B c x^{3} \log \left (x\right ) - 6 \,{\left (B b + A c\right )} x^{2} - 2 \, A a - 3 \,{\left (B a + A b\right )} x}{6 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A)/x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.89868, size = 41, normalized size = 1. \[ B c \log{\left (x \right )} - \frac{2 A a + x^{2} \left (6 A c + 6 B b\right ) + x \left (3 A b + 3 B a\right )}{6 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(c*x**2+b*x+a)/x**4,x)
[Out]
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GIAC/XCAS [A] time = 0.268251, size = 53, normalized size = 1.29 \[ B c{\rm ln}\left ({\left | x \right |}\right ) - \frac{6 \,{\left (B b + A c\right )} x^{2} + 2 \, A a + 3 \,{\left (B a + A b\right )} x}{6 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A)/x^4,x, algorithm="giac")
[Out]