Optimal. Leaf size=22 \[ \log (x) (a B+A b)-\frac{a A}{x}+b B x \]
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Rubi [A] time = 0.0393829, antiderivative size = 22, 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 \[ \log (x) (a B+A b)-\frac{a A}{x}+b B x \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)*(A + B*x))/x^2,x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{A a}{x} + b \int B\, dx + \left (A b + B a\right ) \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(B*x+A)/x**2,x)
[Out]
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Mathematica [A] time = 0.0140815, size = 22, normalized size = 1. \[ \log (x) (a B+A b)-\frac{a A}{x}+b B x \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)*(A + B*x))/x^2,x]
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Maple [A] time = 0.008, size = 23, normalized size = 1.1 \[ bBx+A\ln \left ( x \right ) b+B\ln \left ( x \right ) a-{\frac{Aa}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(B*x+A)/x^2,x)
[Out]
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Maxima [A] time = 1.34666, size = 30, normalized size = 1.36 \[ B b x +{\left (B a + A b\right )} \log \left (x\right ) - \frac{A a}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)/x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.201067, size = 35, normalized size = 1.59 \[ \frac{B b x^{2} +{\left (B a + A b\right )} x \log \left (x\right ) - A a}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)/x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.32623, size = 19, normalized size = 0.86 \[ - \frac{A a}{x} + B b x + \left (A b + B a\right ) \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(B*x+A)/x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.285383, size = 31, normalized size = 1.41 \[ B b x +{\left (B a + A b\right )}{\rm ln}\left ({\left | x \right |}\right ) - \frac{A a}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)/x^2,x, algorithm="giac")
[Out]