Optimal. Leaf size=36 \[ -\frac{a B+A b}{x}-\frac{a A}{2 x^2}+\log (x) (A c+b B)+B c x \]
[Out]
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Rubi [A] time = 0.0653984, antiderivative size = 36, 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 \[ -\frac{a B+A b}{x}-\frac{a A}{2 x^2}+\log (x) (A c+b B)+B c x \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(a + b*x + c*x^2))/x^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{A a}{2 x^{2}} + c \int B\, dx + \left (A c + B b\right ) \log{\left (x \right )} - \frac{A b + B a}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(c*x**2+b*x+a)/x**3,x)
[Out]
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Mathematica [A] time = 0.0362528, size = 37, normalized size = 1.03 \[ \frac{-a B-A b}{x}-\frac{a A}{2 x^2}+\log (x) (A c+b B)+B c x \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(a + b*x + c*x^2))/x^3,x]
[Out]
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Maple [A] time = 0.009, size = 37, normalized size = 1. \[ Bcx+Ac\ln \left ( x \right ) +Bb\ln \left ( x \right ) -{\frac{aA}{2\,{x}^{2}}}-{\frac{Ab}{x}}-{\frac{Ba}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(c*x^2+b*x+a)/x^3,x)
[Out]
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Maxima [A] time = 0.688743, size = 46, normalized size = 1.28 \[ B c x +{\left (B b + A c\right )} \log \left (x\right ) - \frac{A a + 2 \,{\left (B a + A b\right )} x}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A)/x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.269242, size = 55, normalized size = 1.53 \[ \frac{2 \, B c x^{3} + 2 \,{\left (B b + A c\right )} x^{2} \log \left (x\right ) - A a - 2 \,{\left (B a + A b\right )} x}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A)/x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.78463, size = 34, normalized size = 0.94 \[ B c x + \left (A c + B b\right ) \log{\left (x \right )} - \frac{A a + x \left (2 A b + 2 B a\right )}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(c*x**2+b*x+a)/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.272758, size = 47, normalized size = 1.31 \[ B c x +{\left (B b + A c\right )}{\rm ln}\left ({\left | x \right |}\right ) - \frac{A a + 2 \,{\left (B a + A b\right )} x}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A)/x^3,x, algorithm="giac")
[Out]