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 = 0.0706231, antiderivative size = 44, 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 \[ -\frac{a^2 A}{2 x^2}-\frac{a (a B+2 A b)}{x}+b \log (x) (2 a B+A b)+b^2 B x \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)^2*(A + B*x))/x^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{A a^{2}}{2 x^{2}} - \frac{a \left (2 A b + B a\right )}{x} + b^{2} \int B\, dx + b \left (A b + 2 B a\right ) \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**2*(B*x+A)/x**3,x)
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Mathematica [A] time = 0.0403211, 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)^2*(A + B*x))/x^3,x]
[Out]
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Maple [A] time = 0.01, size = 48, normalized size = 1.1 \[{b}^{2}Bx+A\ln \left ( x \right ){b}^{2}+2\,B\ln \left ( x \right ) ab-{\frac{A{a}^{2}}{2\,{x}^{2}}}-2\,{\frac{abA}{x}}-{\frac{{a}^{2}B}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^2*(B*x+A)/x^3,x)
[Out]
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Maxima [A] time = 1.35643, 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*x + A)*(b*x + a)^2/x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.201138, 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*x + A)*(b*x + a)^2/x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.99308, 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)**2*(B*x+A)/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.260705, 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*x + A)*(b*x + a)^2/x^3,x, algorithm="giac")
[Out]