Optimal. Leaf size=33 \[ -\frac{A c+b B}{4 x^4}-\frac{A b}{5 x^5}-\frac{B c}{3 x^3} \]
[Out]
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Rubi [A] time = 0.0395515, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ -\frac{A c+b B}{4 x^4}-\frac{A b}{5 x^5}-\frac{B c}{3 x^3} \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(b*x + c*x^2))/x^7,x]
[Out]
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Rubi in Sympy [A] time = 6.93461, size = 31, normalized size = 0.94 \[ - \frac{A b}{5 x^{5}} - \frac{B c}{3 x^{3}} - \frac{\frac{A c}{4} + \frac{B b}{4}}{x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(c*x**2+b*x)/x**7,x)
[Out]
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Mathematica [A] time = 0.0175523, size = 31, normalized size = 0.94 \[ -\frac{3 A (4 b+5 c x)+5 B x (3 b+4 c x)}{60 x^5} \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(b*x + c*x^2))/x^7,x]
[Out]
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Maple [A] time = 0.006, size = 28, normalized size = 0.9 \[ -{\frac{Ac+Bb}{4\,{x}^{4}}}-{\frac{Bc}{3\,{x}^{3}}}-{\frac{Ab}{5\,{x}^{5}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(c*x^2+b*x)/x^7,x)
[Out]
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Maxima [A] time = 0.696168, size = 36, normalized size = 1.09 \[ -\frac{20 \, B c x^{2} + 12 \, A b + 15 \,{\left (B b + A c\right )} x}{60 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)*(B*x + A)/x^7,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.28463, size = 36, normalized size = 1.09 \[ -\frac{20 \, B c x^{2} + 12 \, A b + 15 \,{\left (B b + A c\right )} x}{60 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)*(B*x + A)/x^7,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.25023, size = 31, normalized size = 0.94 \[ - \frac{12 A b + 20 B c x^{2} + x \left (15 A c + 15 B b\right )}{60 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(c*x**2+b*x)/x**7,x)
[Out]
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GIAC/XCAS [A] time = 0.268401, size = 36, normalized size = 1.09 \[ -\frac{20 \, B c x^{2} + 15 \, B b x + 15 \, A c x + 12 \, A b}{60 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)*(B*x + A)/x^7,x, algorithm="giac")
[Out]