Optimal. Leaf size=33 \[ -\frac{a B+A b}{3 x^3}-\frac{a A}{4 x^4}-\frac{b B}{2 x^2} \]
[Out]
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Rubi [A] time = 0.0437458, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071 \[ -\frac{a B+A b}{3 x^3}-\frac{a A}{4 x^4}-\frac{b B}{2 x^2} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)*(A + B*x))/x^5,x]
[Out]
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Rubi in Sympy [A] time = 9.42148, size = 31, normalized size = 0.94 \[ - \frac{A a}{4 x^{4}} - \frac{B b}{2 x^{2}} - \frac{\frac{A b}{3} + \frac{B a}{3}}{x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(B*x+A)/x**5,x)
[Out]
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Mathematica [A] time = 0.0139481, size = 29, normalized size = 0.88 \[ -\frac{3 a A+4 a B x+4 A b x+6 b B x^2}{12 x^4} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)*(A + B*x))/x^5,x]
[Out]
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Maple [A] time = 0.007, size = 28, normalized size = 0.9 \[ -{\frac{Bb}{2\,{x}^{2}}}-{\frac{Ab+Ba}{3\,{x}^{3}}}-{\frac{Aa}{4\,{x}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(B*x+A)/x^5,x)
[Out]
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Maxima [A] time = 1.34802, size = 36, normalized size = 1.09 \[ -\frac{6 \, B b x^{2} + 3 \, A a + 4 \,{\left (B a + A b\right )} x}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)/x^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.193922, size = 36, normalized size = 1.09 \[ -\frac{6 \, B b x^{2} + 3 \, A a + 4 \,{\left (B a + A b\right )} x}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)/x^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.02201, size = 31, normalized size = 0.94 \[ - \frac{3 A a + 6 B b x^{2} + x \left (4 A b + 4 B a\right )}{12 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(B*x+A)/x**5,x)
[Out]
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GIAC/XCAS [A] time = 0.375601, size = 36, normalized size = 1.09 \[ -\frac{6 \, B b x^{2} + 4 \, B a x + 4 \, A b x + 3 \, A a}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)/x^5,x, algorithm="giac")
[Out]