Optimal. Leaf size=44 \[ -\frac{a^2 A}{2 x^2}-\frac{a (a B+2 A b)}{x}+b \log (x) (2 a B+A b)+b^2 B x \]
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Rubi [A] time = 0.0704439, antiderivative size = 44, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.08 \[ -\frac{a^2 A}{2 x^2}-\frac{a (a B+2 A b)}{x}+b \log (x) (2 a B+A b)+b^2 B x \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^3,x]
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Rubi in Sympy [A] time = 19.6977, size = 41, normalized size = 0.93 \[ - \frac{A a^{2}}{2 x^{2}} + B b^{2} x - \frac{a \left (2 A b + B a\right )}{x} + b \left (A b + 2 B a\right ) \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/x**3,x)
[Out]
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Mathematica [A] time = 0.0441653, size = 43, normalized size = 0.98 \[ -\frac{a^2 (A+2 B x)}{2 x^2}+b \log (x) (2 a B+A b)-\frac{2 a A b}{x}+b^2 B x \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^3,x]
[Out]
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Maple [A] time = 0.008, size = 48, normalized size = 1.1 \[{b}^{2}Bx+A{b}^{2}\ln \left ( x \right ) +2\,B\ln \left ( x \right ) ab-{\frac{A{a}^{2}}{2\,{x}^{2}}}-2\,{\frac{abA}{x}}-{\frac{{a}^{2}B}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(b^2*x^2+2*a*b*x+a^2)/x^3,x)
[Out]
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Maxima [A] time = 0.675507, size = 62, normalized size = 1.41 \[ B b^{2} x +{\left (2 \, B a b + A b^{2}\right )} \log \left (x\right ) - \frac{A a^{2} + 2 \,{\left (B a^{2} + 2 \, A a b\right )} x}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)*(B*x + A)/x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.277055, size = 72, normalized size = 1.64 \[ \frac{2 \, B b^{2} x^{3} + 2 \,{\left (2 \, B a b + A b^{2}\right )} x^{2} \log \left (x\right ) - A a^{2} - 2 \,{\left (B a^{2} + 2 \, A a b\right )} x}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)*(B*x + A)/x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.94092, size = 44, normalized size = 1. \[ B b^{2} x + b \left (A b + 2 B a\right ) \log{\left (x \right )} - \frac{A a^{2} + x \left (4 A a b + 2 B a^{2}\right )}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.267242, size = 63, normalized size = 1.43 \[ B b^{2} x +{\left (2 \, B a b + A b^{2}\right )}{\rm ln}\left ({\left | x \right |}\right ) - \frac{A a^{2} + 2 \,{\left (B a^{2} + 2 \, A a b\right )} x}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)*(B*x + A)/x^3,x, algorithm="giac")
[Out]