Optimal. Leaf size=87 \[ -\frac{a^6 c^5}{10 x^{10}}+\frac{4 a^5 b c^5}{9 x^9}-\frac{5 a^4 b^2 c^5}{8 x^8}+\frac{5 a^2 b^4 c^5}{6 x^6}-\frac{4 a b^5 c^5}{5 x^5}+\frac{b^6 c^5}{4 x^4} \]
[Out]
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Rubi [A] time = 0.0999413, antiderivative size = 87, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{a^6 c^5}{10 x^{10}}+\frac{4 a^5 b c^5}{9 x^9}-\frac{5 a^4 b^2 c^5}{8 x^8}+\frac{5 a^2 b^4 c^5}{6 x^6}-\frac{4 a b^5 c^5}{5 x^5}+\frac{b^6 c^5}{4 x^4} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)*(a*c - b*c*x)^5)/x^11,x]
[Out]
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Rubi in Sympy [A] time = 32.0793, size = 87, normalized size = 1. \[ - \frac{a^{6} c^{5}}{10 x^{10}} + \frac{4 a^{5} b c^{5}}{9 x^{9}} - \frac{5 a^{4} b^{2} c^{5}}{8 x^{8}} + \frac{5 a^{2} b^{4} c^{5}}{6 x^{6}} - \frac{4 a b^{5} c^{5}}{5 x^{5}} + \frac{b^{6} c^{5}}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(-b*c*x+a*c)**5/x**11,x)
[Out]
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Mathematica [A] time = 0.0105546, size = 73, normalized size = 0.84 \[ c^5 \left (-\frac{a^6}{10 x^{10}}+\frac{4 a^5 b}{9 x^9}-\frac{5 a^4 b^2}{8 x^8}+\frac{5 a^2 b^4}{6 x^6}-\frac{4 a b^5}{5 x^5}+\frac{b^6}{4 x^4}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)*(a*c - b*c*x)^5)/x^11,x]
[Out]
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Maple [A] time = 0.007, size = 62, normalized size = 0.7 \[{c}^{5} \left ( -{\frac{5\,{a}^{4}{b}^{2}}{8\,{x}^{8}}}+{\frac{4\,{a}^{5}b}{9\,{x}^{9}}}-{\frac{4\,a{b}^{5}}{5\,{x}^{5}}}-{\frac{{a}^{6}}{10\,{x}^{10}}}+{\frac{{b}^{6}}{4\,{x}^{4}}}+{\frac{5\,{a}^{2}{b}^{4}}{6\,{x}^{6}}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(-b*c*x+a*c)^5/x^11,x)
[Out]
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Maxima [A] time = 1.36719, size = 101, normalized size = 1.16 \[ \frac{90 \, b^{6} c^{5} x^{6} - 288 \, a b^{5} c^{5} x^{5} + 300 \, a^{2} b^{4} c^{5} x^{4} - 225 \, a^{4} b^{2} c^{5} x^{2} + 160 \, a^{5} b c^{5} x - 36 \, a^{6} c^{5}}{360 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^5*(b*x + a)/x^11,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.197007, size = 101, normalized size = 1.16 \[ \frac{90 \, b^{6} c^{5} x^{6} - 288 \, a b^{5} c^{5} x^{5} + 300 \, a^{2} b^{4} c^{5} x^{4} - 225 \, a^{4} b^{2} c^{5} x^{2} + 160 \, a^{5} b c^{5} x - 36 \, a^{6} c^{5}}{360 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^5*(b*x + a)/x^11,x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.05442, size = 80, normalized size = 0.92 \[ \frac{- 36 a^{6} c^{5} + 160 a^{5} b c^{5} x - 225 a^{4} b^{2} c^{5} x^{2} + 300 a^{2} b^{4} c^{5} x^{4} - 288 a b^{5} c^{5} x^{5} + 90 b^{6} c^{5} x^{6}}{360 x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(-b*c*x+a*c)**5/x**11,x)
[Out]
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GIAC/XCAS [A] time = 0.246342, size = 101, normalized size = 1.16 \[ \frac{90 \, b^{6} c^{5} x^{6} - 288 \, a b^{5} c^{5} x^{5} + 300 \, a^{2} b^{4} c^{5} x^{4} - 225 \, a^{4} b^{2} c^{5} x^{2} + 160 \, a^{5} b c^{5} x - 36 \, a^{6} c^{5}}{360 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(b*c*x - a*c)^5*(b*x + a)/x^11,x, algorithm="giac")
[Out]