Optimal. Leaf size=38 \[ x (a B+A b)+a A \log (x)+\frac{1}{2} x^2 (A c+b B)+\frac{1}{3} B c x^3 \]
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Rubi [A] time = 0.0539495, antiderivative size = 38, 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 \[ x (a B+A b)+a A \log (x)+\frac{1}{2} x^2 (A c+b B)+\frac{1}{3} B c x^3 \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(a + b*x + c*x^2))/x,x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ A a \log{\left (x \right )} + \frac{B c x^{3}}{3} + a \int B\, dx + b \int A\, dx + \left (A c + B b\right ) \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(c*x**2+b*x+a)/x,x)
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Mathematica [A] time = 0.0185459, size = 38, normalized size = 1. \[ x (a B+A b)+a A \log (x)+\frac{1}{2} x^2 (A c+b B)+\frac{1}{3} B c x^3 \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(a + b*x + c*x^2))/x,x]
[Out]
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Maple [A] time = 0.004, size = 36, normalized size = 1. \[{\frac{Bc{x}^{3}}{3}}+{\frac{Ac{x}^{2}}{2}}+{\frac{Bb{x}^{2}}{2}}+Abx+aBx+aA\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(c*x^2+b*x+a)/x,x)
[Out]
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Maxima [A] time = 0.690837, size = 46, normalized size = 1.21 \[ \frac{1}{3} \, B c x^{3} + \frac{1}{2} \,{\left (B b + A c\right )} x^{2} + A a \log \left (x\right ) +{\left (B a + A b\right )} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A)/x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.266694, size = 46, normalized size = 1.21 \[ \frac{1}{3} \, B c x^{3} + \frac{1}{2} \,{\left (B b + A c\right )} x^{2} + A a \log \left (x\right ) +{\left (B a + A b\right )} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A)/x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.10449, size = 36, normalized size = 0.95 \[ A a \log{\left (x \right )} + \frac{B c x^{3}}{3} + x^{2} \left (\frac{A c}{2} + \frac{B b}{2}\right ) + x \left (A b + B a\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(c*x**2+b*x+a)/x,x)
[Out]
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GIAC/XCAS [A] time = 0.268484, size = 49, normalized size = 1.29 \[ \frac{1}{3} \, B c x^{3} + \frac{1}{2} \, B b x^{2} + \frac{1}{2} \, A c x^{2} + B a x + A b x + A a{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A)/x,x, algorithm="giac")
[Out]