Optimal. Leaf size=31 \[ -\frac{a B+A b}{2 x^2}-\frac{a A}{3 x^3}-\frac{b B}{x} \]
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Rubi [A] time = 0.0418669, antiderivative size = 31, 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 \[ -\frac{a B+A b}{2 x^2}-\frac{a A}{3 x^3}-\frac{b B}{x} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)*(A + B*x))/x^4,x]
[Out]
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Rubi in Sympy [A] time = 9.64497, size = 27, normalized size = 0.87 \[ - \frac{A a}{3 x^{3}} - \frac{B b}{x} - \frac{\frac{A b}{2} + \frac{B a}{2}}{x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(B*x+A)/x**4,x)
[Out]
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Mathematica [A] time = 0.0151285, size = 28, normalized size = 0.9 \[ -\frac{a (2 A+3 B x)+3 b x (A+2 B x)}{6 x^3} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)*(A + B*x))/x^4,x]
[Out]
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Maple [A] time = 0.007, size = 28, normalized size = 0.9 \[ -{\frac{Ab+Ba}{2\,{x}^{2}}}-{\frac{Bb}{x}}-{\frac{Aa}{3\,{x}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(B*x+A)/x^4,x)
[Out]
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Maxima [A] time = 1.34636, size = 36, normalized size = 1.16 \[ -\frac{6 \, B b x^{2} + 2 \, A a + 3 \,{\left (B a + A b\right )} x}{6 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)/x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.194757, size = 36, normalized size = 1.16 \[ -\frac{6 \, B b x^{2} + 2 \, A a + 3 \,{\left (B a + A b\right )} x}{6 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)/x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.78957, size = 31, normalized size = 1. \[ - \frac{2 A a + 6 B b x^{2} + x \left (3 A b + 3 B a\right )}{6 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(B*x+A)/x**4,x)
[Out]
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GIAC/XCAS [A] time = 0.317351, size = 36, normalized size = 1.16 \[ -\frac{6 \, B b x^{2} + 3 \, B a x + 3 \, A b x + 2 \, A a}{6 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)/x^4,x, algorithm="giac")
[Out]