Optimal. Leaf size=45 \[ -\frac{a B+A b}{3 x^3}-\frac{a A}{4 x^4}-\frac{A c+b B}{2 x^2}-\frac{B c}{x} \]
[Out]
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Rubi [A] time = 0.0651623, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053 \[ -\frac{a B+A b}{3 x^3}-\frac{a A}{4 x^4}-\frac{A c+b B}{2 x^2}-\frac{B c}{x} \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(a + b*x + c*x^2))/x^5,x]
[Out]
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Rubi in Sympy [A] time = 9.70543, size = 41, normalized size = 0.91 \[ - \frac{A a}{4 x^{4}} - \frac{B c}{x} - \frac{\frac{A c}{2} + \frac{B b}{2}}{x^{2}} - \frac{\frac{A b}{3} + \frac{B a}{3}}{x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(c*x**2+b*x+a)/x**5,x)
[Out]
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Mathematica [A] time = 0.0264936, size = 42, normalized size = 0.93 \[ -\frac{a (3 A+4 B x)+2 x (A (2 b+3 c x)+3 B x (b+2 c x))}{12 x^4} \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(a + b*x + c*x^2))/x^5,x]
[Out]
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Maple [A] time = 0.007, size = 40, normalized size = 0.9 \[ -{\frac{aA}{4\,{x}^{4}}}-{\frac{Ab+Ba}{3\,{x}^{3}}}-{\frac{Ac+Bb}{2\,{x}^{2}}}-{\frac{Bc}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(c*x^2+b*x+a)/x^5,x)
[Out]
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Maxima [A] time = 0.699749, size = 53, normalized size = 1.18 \[ -\frac{12 \, B c x^{3} + 6 \,{\left (B b + A c\right )} x^{2} + 3 \, A a + 4 \,{\left (B a + A b\right )} x}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A)/x^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.306345, size = 53, normalized size = 1.18 \[ -\frac{12 \, B c x^{3} + 6 \,{\left (B b + A c\right )} x^{2} + 3 \, A a + 4 \,{\left (B a + A b\right )} x}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A)/x^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.57781, size = 44, normalized size = 0.98 \[ - \frac{3 A a + 12 B c x^{3} + x^{2} \left (6 A c + 6 B b\right ) + x \left (4 A b + 4 B a\right )}{12 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(c*x**2+b*x+a)/x**5,x)
[Out]
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GIAC/XCAS [A] time = 0.267853, size = 55, normalized size = 1.22 \[ -\frac{12 \, B c x^{3} + 6 \, B b x^{2} + 6 \, A c x^{2} + 4 \, B a x + 4 \, A b x + 3 \, A a}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x + a)*(B*x + A)/x^5,x, algorithm="giac")
[Out]