Optimal. Leaf size=89 \[ -\frac{13 b^3 c^6 (a-b x)^7}{2520 a^3 x^7}-\frac{13 b^2 c^6 (a-b x)^7}{360 a^2 x^8}-\frac{c^6 (a-b x)^7}{10 x^{10}}-\frac{13 b c^6 (a-b x)^7}{90 a x^9} \]
[Out]
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Rubi [A] time = 0.0972803, antiderivative size = 89, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.15 \[ -\frac{13 b^3 c^6 (a-b x)^7}{2520 a^3 x^7}-\frac{13 b^2 c^6 (a-b x)^7}{360 a^2 x^8}-\frac{c^6 (a-b x)^7}{10 x^{10}}-\frac{13 b c^6 (a-b x)^7}{90 a x^9} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)*(a*c - b*c*x)^6)/x^11,x]
[Out]
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Rubi in Sympy [A] time = 24.7376, size = 83, normalized size = 0.93 \[ - \frac{c^{6} \left (a - b x\right )^{7}}{10 x^{10}} - \frac{13 b c^{6} \left (a - b x\right )^{7}}{90 a x^{9}} - \frac{13 b^{2} c^{6} \left (a - b x\right )^{7}}{360 a^{2} x^{8}} - \frac{13 b^{3} c^{6} \left (a - b x\right )^{7}}{2520 a^{3} x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*(-b*c*x+a*c)**6/x**11,x)
[Out]
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Mathematica [A] time = 0.0135778, size = 119, normalized size = 1.34 \[ -\frac{a^7 c^6}{10 x^{10}}+\frac{5 a^6 b c^6}{9 x^9}-\frac{9 a^5 b^2 c^6}{8 x^8}+\frac{5 a^4 b^3 c^6}{7 x^7}+\frac{5 a^3 b^4 c^6}{6 x^6}-\frac{9 a^2 b^5 c^6}{5 x^5}+\frac{5 a b^6 c^6}{4 x^4}-\frac{b^7 c^6}{3 x^3} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)*(a*c - b*c*x)^6)/x^11,x]
[Out]
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Maple [A] time = 0.009, size = 84, normalized size = 0.9 \[{c}^{6} \left ( -{\frac{9\,{a}^{5}{b}^{2}}{8\,{x}^{8}}}+{\frac{5\,{a}^{4}{b}^{3}}{7\,{x}^{7}}}+{\frac{5\,{a}^{6}b}{9\,{x}^{9}}}-{\frac{9\,{a}^{2}{b}^{5}}{5\,{x}^{5}}}-{\frac{{a}^{7}}{10\,{x}^{10}}}-{\frac{{b}^{7}}{3\,{x}^{3}}}+{\frac{5\,a{b}^{6}}{4\,{x}^{4}}}+{\frac{5\,{a}^{3}{b}^{4}}{6\,{x}^{6}}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*(-b*c*x+a*c)^6/x^11,x)
[Out]
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Maxima [A] time = 1.35529, size = 139, normalized size = 1.56 \[ -\frac{840 \, b^{7} c^{6} x^{7} - 3150 \, a b^{6} c^{6} x^{6} + 4536 \, a^{2} b^{5} c^{6} x^{5} - 2100 \, a^{3} b^{4} c^{6} x^{4} - 1800 \, a^{4} b^{3} c^{6} x^{3} + 2835 \, a^{5} b^{2} c^{6} x^{2} - 1400 \, a^{6} b c^{6} x + 252 \, a^{7} c^{6}}{2520 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x - a*c)^6*(b*x + a)/x^11,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.200069, size = 139, normalized size = 1.56 \[ -\frac{840 \, b^{7} c^{6} x^{7} - 3150 \, a b^{6} c^{6} x^{6} + 4536 \, a^{2} b^{5} c^{6} x^{5} - 2100 \, a^{3} b^{4} c^{6} x^{4} - 1800 \, a^{4} b^{3} c^{6} x^{3} + 2835 \, a^{5} b^{2} c^{6} x^{2} - 1400 \, a^{6} b c^{6} x + 252 \, a^{7} c^{6}}{2520 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x - a*c)^6*(b*x + a)/x^11,x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.71471, size = 112, normalized size = 1.26 \[ - \frac{252 a^{7} c^{6} - 1400 a^{6} b c^{6} x + 2835 a^{5} b^{2} c^{6} x^{2} - 1800 a^{4} b^{3} c^{6} x^{3} - 2100 a^{3} b^{4} c^{6} x^{4} + 4536 a^{2} b^{5} c^{6} x^{5} - 3150 a b^{6} c^{6} x^{6} + 840 b^{7} c^{6} x^{7}}{2520 x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*(-b*c*x+a*c)**6/x**11,x)
[Out]
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GIAC/XCAS [A] time = 0.237591, size = 139, normalized size = 1.56 \[ -\frac{840 \, b^{7} c^{6} x^{7} - 3150 \, a b^{6} c^{6} x^{6} + 4536 \, a^{2} b^{5} c^{6} x^{5} - 2100 \, a^{3} b^{4} c^{6} x^{4} - 1800 \, a^{4} b^{3} c^{6} x^{3} + 2835 \, a^{5} b^{2} c^{6} x^{2} - 1400 \, a^{6} b c^{6} x + 252 \, a^{7} c^{6}}{2520 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*c*x - a*c)^6*(b*x + a)/x^11,x, algorithm="giac")
[Out]