Optimal. Leaf size=26 \[ -\frac{a A}{2 x^2}-\frac{a B}{x}+A c \log (x)+B c x \]
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Rubi [A] time = 0.0417559, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ -\frac{a A}{2 x^2}-\frac{a B}{x}+A c \log (x)+B c x \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(a + c*x^2))/x^3,x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{A a}{2 x^{2}} + A c \log{\left (x \right )} - \frac{B a}{x} + c \int B\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(c*x**2+a)/x**3,x)
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Mathematica [A] time = 0.00730489, size = 26, normalized size = 1. \[ -\frac{a A}{2 x^2}-\frac{a B}{x}+A c \log (x)+B c x \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(a + c*x^2))/x^3,x]
[Out]
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Maple [A] time = 0.009, size = 25, normalized size = 1. \[ -{\frac{aA}{2\,{x}^{2}}}-{\frac{Ba}{x}}+Bcx+Ac\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(c*x^2+a)/x^3,x)
[Out]
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Maxima [A] time = 0.684125, size = 32, normalized size = 1.23 \[ B c x + A c \log \left (x\right ) - \frac{2 \, B a x + A a}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)*(B*x + A)/x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.291383, size = 42, normalized size = 1.62 \[ \frac{2 \, B c x^{3} + 2 \, A c x^{2} \log \left (x\right ) - 2 \, B a x - A a}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)*(B*x + A)/x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.39434, size = 26, normalized size = 1. \[ A c \log{\left (x \right )} + B c x - \frac{A a + 2 B a x}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(c*x**2+a)/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.271655, size = 34, normalized size = 1.31 \[ B c x + A c{\rm ln}\left ({\left | x \right |}\right ) - \frac{2 \, B a x + A a}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)*(B*x + A)/x^3,x, algorithm="giac")
[Out]