Optimal. Leaf size=44 \[ \frac{(a+b x)^4 (A b-5 a B)}{20 a^2 x^4}-\frac{A (a+b x)^4}{5 a x^5} \]
[Out]
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Rubi [A] time = 0.0553299, antiderivative size = 44, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ \frac{(a+b x)^4 (A b-5 a B)}{20 a^2 x^4}-\frac{A (a+b x)^4}{5 a x^5} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)^3*(A + B*x))/x^6,x]
[Out]
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Rubi in Sympy [A] time = 21.342, size = 65, normalized size = 1.48 \[ - \frac{A a^{3}}{5 x^{5}} - \frac{B b^{3}}{x} - \frac{a^{2} \left (3 A b + B a\right )}{4 x^{4}} - \frac{a b \left (A b + B a\right )}{x^{3}} - \frac{b^{2} \left (A b + 3 B a\right )}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**3*(B*x+A)/x**6,x)
[Out]
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Mathematica [A] time = 0.032885, size = 66, normalized size = 1.5 \[ -\frac{a^3 (4 A+5 B x)+5 a^2 b x (3 A+4 B x)+10 a b^2 x^2 (2 A+3 B x)+10 b^3 x^3 (A+2 B x)}{20 x^5} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)^3*(A + B*x))/x^6,x]
[Out]
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Maple [A] time = 0.007, size = 66, normalized size = 1.5 \[ -{\frac{{b}^{2} \left ( Ab+3\,Ba \right ) }{2\,{x}^{2}}}-{\frac{A{a}^{3}}{5\,{x}^{5}}}-{\frac{B{b}^{3}}{x}}-{\frac{ab \left ( Ab+Ba \right ) }{{x}^{3}}}-{\frac{{a}^{2} \left ( 3\,Ab+Ba \right ) }{4\,{x}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^3*(B*x+A)/x^6,x)
[Out]
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Maxima [A] time = 1.35107, size = 99, normalized size = 2.25 \[ -\frac{20 \, B b^{3} x^{4} + 4 \, A a^{3} + 10 \,{\left (3 \, B a b^{2} + A b^{3}\right )} x^{3} + 20 \,{\left (B a^{2} b + A a b^{2}\right )} x^{2} + 5 \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x}{20 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^3/x^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.197189, size = 99, normalized size = 2.25 \[ -\frac{20 \, B b^{3} x^{4} + 4 \, A a^{3} + 10 \,{\left (3 \, B a b^{2} + A b^{3}\right )} x^{3} + 20 \,{\left (B a^{2} b + A a b^{2}\right )} x^{2} + 5 \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x}{20 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^3/x^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.71446, size = 78, normalized size = 1.77 \[ - \frac{4 A a^{3} + 20 B b^{3} x^{4} + x^{3} \left (10 A b^{3} + 30 B a b^{2}\right ) + x^{2} \left (20 A a b^{2} + 20 B a^{2} b\right ) + x \left (15 A a^{2} b + 5 B a^{3}\right )}{20 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**3*(B*x+A)/x**6,x)
[Out]
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GIAC/XCAS [A] time = 0.414367, size = 101, normalized size = 2.3 \[ -\frac{20 \, B b^{3} x^{4} + 30 \, B a b^{2} x^{3} + 10 \, A b^{3} x^{3} + 20 \, B a^{2} b x^{2} + 20 \, A a b^{2} x^{2} + 5 \, B a^{3} x + 15 \, A a^{2} b x + 4 \, A a^{3}}{20 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^3/x^6,x, algorithm="giac")
[Out]