Optimal. Leaf size=45 \[ -\frac{(b+c x)^4 (5 b B-A c)}{20 b^2 x^4}-\frac{A (b+c x)^4}{5 b x^5} \]
[Out]
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Rubi [A] time = 0.0677126, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.15 \[ -\frac{(b+c x)^4 (5 b B-A c)}{20 b^2 x^4}-\frac{A (b+c x)^4}{5 b x^5} \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(b*x + c*x^2)^3)/x^9,x]
[Out]
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Rubi in Sympy [A] time = 15.238, size = 65, normalized size = 1.44 \[ - \frac{A b^{3}}{5 x^{5}} - \frac{B c^{3}}{x} - \frac{b^{2} \left (3 A c + B b\right )}{4 x^{4}} - \frac{b c \left (A c + B b\right )}{x^{3}} - \frac{c^{2} \left (A c + 3 B b\right )}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(c*x**2+b*x)**3/x**9,x)
[Out]
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Mathematica [A] time = 0.0353892, size = 72, normalized size = 1.6 \[ -\frac{A \left (4 b^3+15 b^2 c x+20 b c^2 x^2+10 c^3 x^3\right )+5 B x \left (b^3+4 b^2 c x+6 b c^2 x^2+4 c^3 x^3\right )}{20 x^5} \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(b*x + c*x^2)^3)/x^9,x]
[Out]
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Maple [A] time = 0.008, size = 66, normalized size = 1.5 \[ -{\frac{{b}^{2} \left ( 3\,Ac+Bb \right ) }{4\,{x}^{4}}}-{\frac{bc \left ( Ac+Bb \right ) }{{x}^{3}}}-{\frac{{c}^{2} \left ( Ac+3\,Bb \right ) }{2\,{x}^{2}}}-{\frac{A{b}^{3}}{5\,{x}^{5}}}-{\frac{B{c}^{3}}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(c*x^2+b*x)^3/x^9,x)
[Out]
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Maxima [A] time = 0.710597, size = 99, normalized size = 2.2 \[ -\frac{20 \, B c^{3} x^{4} + 4 \, A b^{3} + 10 \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{3} + 20 \,{\left (B b^{2} c + A b c^{2}\right )} x^{2} + 5 \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x}{20 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)/x^9,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.268187, size = 99, normalized size = 2.2 \[ -\frac{20 \, B c^{3} x^{4} + 4 \, A b^{3} + 10 \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{3} + 20 \,{\left (B b^{2} c + A b c^{2}\right )} x^{2} + 5 \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x}{20 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)/x^9,x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.72578, size = 78, normalized size = 1.73 \[ - \frac{4 A b^{3} + 20 B c^{3} x^{4} + x^{3} \left (10 A c^{3} + 30 B b c^{2}\right ) + x^{2} \left (20 A b c^{2} + 20 B b^{2} c\right ) + x \left (15 A b^{2} c + 5 B b^{3}\right )}{20 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(c*x**2+b*x)**3/x**9,x)
[Out]
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GIAC/XCAS [A] time = 0.268744, size = 101, normalized size = 2.24 \[ -\frac{20 \, B c^{3} x^{4} + 30 \, B b c^{2} x^{3} + 10 \, A c^{3} x^{3} + 20 \, B b^{2} c x^{2} + 20 \, A b c^{2} x^{2} + 5 \, B b^{3} x + 15 \, A b^{2} c x + 4 \, A b^{3}}{20 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(B*x + A)/x^9,x, algorithm="giac")
[Out]