Optimal. Leaf size=59 \[ -\frac{A (b+c x)^4}{4 b x^4}-\frac{b^3 B}{3 x^3}-\frac{3 b^2 B c}{2 x^2}-\frac{3 b B c^2}{x}+B c^3 \log (x) \]
[Out]
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Rubi [A] time = 0.0671478, antiderivative size = 59, 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 \[ -\frac{A (b+c x)^4}{4 b x^4}-\frac{b^3 B}{3 x^3}-\frac{3 b^2 B c}{2 x^2}-\frac{3 b B c^2}{x}+B c^3 \log (x) \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(b*x + c*x^2)^3)/x^8,x]
[Out]
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Rubi in Sympy [A] time = 10.7718, size = 56, normalized size = 0.95 \[ - \frac{A \left (b + c x\right )^{4}}{4 b x^{4}} - \frac{B b^{3}}{3 x^{3}} - \frac{3 B b^{2} c}{2 x^{2}} - \frac{3 B b c^{2}}{x} + B c^{3} \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(c*x**2+b*x)**3/x**8,x)
[Out]
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Mathematica [A] time = 0.0660893, size = 71, normalized size = 1.2 \[ B c^3 \log (x)-\frac{3 A \left (b^3+4 b^2 c x+6 b c^2 x^2+4 c^3 x^3\right )+2 b B x \left (2 b^2+9 b c x+18 c^2 x^2\right )}{12 x^4} \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(b*x + c*x^2)^3)/x^8,x]
[Out]
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Maple [A] time = 0.009, size = 76, normalized size = 1.3 \[ B{c}^{3}\ln \left ( x \right ) -{\frac{A{b}^{3}}{4\,{x}^{4}}}-{\frac{A{b}^{2}c}{{x}^{3}}}-{\frac{B{b}^{3}}{3\,{x}^{3}}}-{\frac{3\,Ab{c}^{2}}{2\,{x}^{2}}}-{\frac{3\,B{b}^{2}c}{2\,{x}^{2}}}-{\frac{A{c}^{3}}{x}}-3\,{\frac{Bb{c}^{2}}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(c*x^2+b*x)^3/x^8,x)
[Out]
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Maxima [A] time = 0.70031, size = 97, normalized size = 1.64 \[ B c^{3} \log \left (x\right ) - \frac{3 \, A b^{3} + 12 \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{3} + 18 \,{\left (B b^{2} c + A b c^{2}\right )} x^{2} + 4 \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)/x^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.265271, size = 101, normalized size = 1.71 \[ \frac{12 \, B c^{3} x^{4} \log \left (x\right ) - 3 \, A b^{3} - 12 \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{3} - 18 \,{\left (B b^{2} c + A b c^{2}\right )} x^{2} - 4 \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)/x^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.48803, size = 75, normalized size = 1.27 \[ B c^{3} \log{\left (x \right )} - \frac{3 A b^{3} + x^{3} \left (12 A c^{3} + 36 B b c^{2}\right ) + x^{2} \left (18 A b c^{2} + 18 B b^{2} c\right ) + x \left (12 A b^{2} c + 4 B b^{3}\right )}{12 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(c*x**2+b*x)**3/x**8,x)
[Out]
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GIAC/XCAS [A] time = 0.271532, size = 99, normalized size = 1.68 \[ B c^{3}{\rm ln}\left ({\left | x \right |}\right ) - \frac{3 \, A b^{3} + 12 \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{3} + 18 \,{\left (B b^{2} c + A b c^{2}\right )} x^{2} + 4 \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)/x^8,x, algorithm="giac")
[Out]