Optimal. Leaf size=105 \[ -\frac{a^5 A}{x}+a^4 \log (x) (a B+5 A b)+5 a^3 b x (a B+2 A b)+5 a^2 b^2 x^2 (a B+A b)+\frac{1}{4} b^4 x^4 (5 a B+A b)+\frac{5}{3} a b^3 x^3 (2 a B+A b)+\frac{1}{5} b^5 B x^5 \]
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Rubi [A] time = 0.187493, antiderivative size = 105, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ -\frac{a^5 A}{x}+a^4 \log (x) (a B+5 A b)+5 a^3 b x (a B+2 A b)+5 a^2 b^2 x^2 (a B+A b)+\frac{1}{4} b^4 x^4 (5 a B+A b)+\frac{5}{3} a b^3 x^3 (2 a B+A b)+\frac{1}{5} b^5 B x^5 \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)^5*(A + B*x))/x^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{A a^{5}}{x} + \frac{B b^{5} x^{5}}{5} + a^{4} \left (5 A b + B a\right ) \log{\left (x \right )} + 5 a^{3} b x \left (2 A b + B a\right ) + 10 a^{2} b^{2} \left (A b + B a\right ) \int x\, dx + \frac{5 a b^{3} x^{3} \left (A b + 2 B a\right )}{3} + \frac{b^{4} x^{4} \left (A b + 5 B a\right )}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**5*(B*x+A)/x**2,x)
[Out]
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Mathematica [A] time = 0.0722995, size = 107, normalized size = 1.02 \[ -\frac{a^5 A}{x}+5 a^3 b x (a B+2 A b)+5 a^2 b^2 x^2 (a B+A b)+\log (x) \left (a^5 B+5 a^4 A b\right )+\frac{1}{4} b^4 x^4 (5 a B+A b)+\frac{5}{3} a b^3 x^3 (2 a B+A b)+\frac{1}{5} b^5 B x^5 \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)^5*(A + B*x))/x^2,x]
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Maple [A] time = 0.01, size = 119, normalized size = 1.1 \[{\frac{{b}^{5}B{x}^{5}}{5}}+{\frac{A{x}^{4}{b}^{5}}{4}}+{\frac{5\,B{x}^{4}a{b}^{4}}{4}}+{\frac{5\,A{x}^{3}a{b}^{4}}{3}}+{\frac{10\,B{x}^{3}{a}^{2}{b}^{3}}{3}}+5\,A{x}^{2}{a}^{2}{b}^{3}+5\,B{x}^{2}{a}^{3}{b}^{2}+10\,Ax{a}^{3}{b}^{2}+5\,Bx{a}^{4}b+5\,A\ln \left ( x \right ){a}^{4}b+B\ln \left ( x \right ){a}^{5}-{\frac{A{a}^{5}}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^5*(B*x+A)/x^2,x)
[Out]
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Maxima [A] time = 1.3535, size = 155, normalized size = 1.48 \[ \frac{1}{5} \, B b^{5} x^{5} - \frac{A a^{5}}{x} + \frac{1}{4} \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{4} + \frac{5}{3} \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{3} + 5 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{2} + 5 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x +{\left (B a^{5} + 5 \, A a^{4} b\right )} \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^5/x^2,x, algorithm="maxima")
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Fricas [A] time = 0.200399, size = 163, normalized size = 1.55 \[ \frac{12 \, B b^{5} x^{6} - 60 \, A a^{5} + 15 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{5} + 100 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{4} + 300 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{3} + 300 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{2} + 60 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x \log \left (x\right )}{60 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^5/x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.82058, size = 121, normalized size = 1.15 \[ - \frac{A a^{5}}{x} + \frac{B b^{5} x^{5}}{5} + a^{4} \left (5 A b + B a\right ) \log{\left (x \right )} + x^{4} \left (\frac{A b^{5}}{4} + \frac{5 B a b^{4}}{4}\right ) + x^{3} \left (\frac{5 A a b^{4}}{3} + \frac{10 B a^{2} b^{3}}{3}\right ) + x^{2} \left (5 A a^{2} b^{3} + 5 B a^{3} b^{2}\right ) + x \left (10 A a^{3} b^{2} + 5 B a^{4} b\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**5*(B*x+A)/x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.257819, size = 161, normalized size = 1.53 \[ \frac{1}{5} \, B b^{5} x^{5} + \frac{5}{4} \, B a b^{4} x^{4} + \frac{1}{4} \, A b^{5} x^{4} + \frac{10}{3} \, B a^{2} b^{3} x^{3} + \frac{5}{3} \, A a b^{4} x^{3} + 5 \, B a^{3} b^{2} x^{2} + 5 \, A a^{2} b^{3} x^{2} + 5 \, B a^{4} b x + 10 \, A a^{3} b^{2} x - \frac{A a^{5}}{x} +{\left (B a^{5} + 5 \, A a^{4} b\right )}{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^5/x^2,x, algorithm="giac")
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