Optimal. Leaf size=40 \[ A b^2 \log (x)+2 A b c x+\frac{1}{2} A c^2 x^2+\frac{B (b+c x)^3}{3 c} \]
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Rubi [A] time = 0.0536276, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.15 \[ A b^2 \log (x)+2 A b c x+\frac{1}{2} A c^2 x^2+\frac{B (b+c x)^3}{3 c} \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(b*x + c*x^2)^2)/x^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ A b^{2} \log{\left (x \right )} + 2 A b c x + A c^{2} \int x\, dx + \frac{B \left (b + c x\right )^{3}}{3 c} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(c*x**2+b*x)**2/x**3,x)
[Out]
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Mathematica [A] time = 0.0268239, size = 43, normalized size = 1.08 \[ A b^2 \log (x)+b c x (2 A+B x)+\frac{1}{6} c^2 x^2 (3 A+2 B x)+b^2 B x \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(b*x + c*x^2)^2)/x^3,x]
[Out]
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Maple [A] time = 0.003, size = 46, normalized size = 1.2 \[{\frac{B{c}^{2}{x}^{3}}{3}}+{\frac{A{c}^{2}{x}^{2}}{2}}+B{x}^{2}bc+2\,Abcx+{b}^{2}Bx+A{b}^{2}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(c*x^2+b*x)^2/x^3,x)
[Out]
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Maxima [A] time = 0.69917, size = 62, normalized size = 1.55 \[ \frac{1}{3} \, B c^{2} x^{3} + A b^{2} \log \left (x\right ) + \frac{1}{2} \,{\left (2 \, B b c + A c^{2}\right )} x^{2} +{\left (B b^{2} + 2 \, A b c\right )} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^2*(B*x + A)/x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.270684, size = 62, normalized size = 1.55 \[ \frac{1}{3} \, B c^{2} x^{3} + A b^{2} \log \left (x\right ) + \frac{1}{2} \,{\left (2 \, B b c + A c^{2}\right )} x^{2} +{\left (B b^{2} + 2 \, A b c\right )} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^2*(B*x + A)/x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.21555, size = 46, normalized size = 1.15 \[ A b^{2} \log{\left (x \right )} + \frac{B c^{2} x^{3}}{3} + x^{2} \left (\frac{A c^{2}}{2} + B b c\right ) + x \left (2 A b c + B b^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(c*x**2+b*x)**2/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.266865, size = 62, normalized size = 1.55 \[ \frac{1}{3} \, B c^{2} x^{3} + B b c x^{2} + \frac{1}{2} \, A c^{2} x^{2} + B b^{2} x + 2 \, A b c x + A b^{2}{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^2*(B*x + A)/x^3,x, algorithm="giac")
[Out]