Optimal. Leaf size=24 \[ x (a B+A b)+a A \log (x)+\frac{1}{2} b B x^2 \]
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Rubi [A] time = 0.0299539, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071 \[ x (a B+A b)+a A \log (x)+\frac{1}{2} b B x^2 \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)*(A + B*x))/x,x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ A a \log{\left (x \right )} + B b \int x\, dx + a \int B\, dx + b \int A\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(B*x+A)/x,x)
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Mathematica [A] time = 0.00790774, size = 24, normalized size = 1. \[ x (a B+A b)+a A \log (x)+\frac{1}{2} b B x^2 \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)*(A + B*x))/x,x]
[Out]
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Maple [A] time = 0.003, size = 22, normalized size = 0.9 \[{\frac{bB{x}^{2}}{2}}+Abx+Bax+aA\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(B*x+A)/x,x)
[Out]
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Maxima [A] time = 1.3494, size = 30, normalized size = 1.25 \[ \frac{1}{2} \, B b x^{2} + A a \log \left (x\right ) +{\left (B a + A b\right )} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)/x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.20254, size = 30, normalized size = 1.25 \[ \frac{1}{2} \, B b x^{2} + A a \log \left (x\right ) +{\left (B a + A b\right )} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)/x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.11974, size = 22, normalized size = 0.92 \[ A a \log{\left (x \right )} + \frac{B b x^{2}}{2} + x \left (A b + B a\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(B*x+A)/x,x)
[Out]
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GIAC/XCAS [A] time = 0.288064, size = 30, normalized size = 1.25 \[ \frac{1}{2} \, B b x^{2} + B a x + A b x + A a{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)/x,x, algorithm="giac")
[Out]