Optimal. Leaf size=64 \[ -\frac{b^3 (a x+b)^9}{9 a^4}+\frac{3 b^2 (a x+b)^{10}}{10 a^4}+\frac{(a x+b)^{12}}{12 a^4}-\frac{3 b (a x+b)^{11}}{11 a^4} \]
[Out]
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Rubi [A] time = 0.0922738, antiderivative size = 64, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\frac{b^3 (a x+b)^9}{9 a^4}+\frac{3 b^2 (a x+b)^{10}}{10 a^4}+\frac{(a x+b)^{12}}{12 a^4}-\frac{3 b (a x+b)^{11}}{11 a^4} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^8*x^11,x]
[Out]
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Rubi in Sympy [A] time = 18.378, size = 58, normalized size = 0.91 \[ - \frac{b^{3} \left (a x + b\right )^{9}}{9 a^{4}} + \frac{3 b^{2} \left (a x + b\right )^{10}}{10 a^{4}} - \frac{3 b \left (a x + b\right )^{11}}{11 a^{4}} + \frac{\left (a x + b\right )^{12}}{12 a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**8*x**11,x)
[Out]
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Mathematica [A] time = 0.00468903, size = 106, normalized size = 1.66 \[ \frac{a^8 x^{12}}{12}+\frac{8}{11} a^7 b x^{11}+\frac{14}{5} a^6 b^2 x^{10}+\frac{56}{9} a^5 b^3 x^9+\frac{35}{4} a^4 b^4 x^8+8 a^3 b^5 x^7+\frac{14}{3} a^2 b^6 x^6+\frac{8}{5} a b^7 x^5+\frac{b^8 x^4}{4} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^8*x^11,x]
[Out]
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Maple [A] time = 0.001, size = 91, normalized size = 1.4 \[{\frac{{a}^{8}{x}^{12}}{12}}+{\frac{8\,{a}^{7}b{x}^{11}}{11}}+{\frac{14\,{a}^{6}{b}^{2}{x}^{10}}{5}}+{\frac{56\,{a}^{5}{b}^{3}{x}^{9}}{9}}+{\frac{35\,{a}^{4}{b}^{4}{x}^{8}}{4}}+8\,{a}^{3}{b}^{5}{x}^{7}+{\frac{14\,{a}^{2}{b}^{6}{x}^{6}}{3}}+{\frac{8\,a{b}^{7}{x}^{5}}{5}}+{\frac{{b}^{8}{x}^{4}}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^8*x^11,x)
[Out]
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Maxima [A] time = 1.4361, size = 122, normalized size = 1.91 \[ \frac{1}{12} \, a^{8} x^{12} + \frac{8}{11} \, a^{7} b x^{11} + \frac{14}{5} \, a^{6} b^{2} x^{10} + \frac{56}{9} \, a^{5} b^{3} x^{9} + \frac{35}{4} \, a^{4} b^{4} x^{8} + 8 \, a^{3} b^{5} x^{7} + \frac{14}{3} \, a^{2} b^{6} x^{6} + \frac{8}{5} \, a b^{7} x^{5} + \frac{1}{4} \, b^{8} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8*x^11,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211117, size = 122, normalized size = 1.91 \[ \frac{1}{12} \, a^{8} x^{12} + \frac{8}{11} \, a^{7} b x^{11} + \frac{14}{5} \, a^{6} b^{2} x^{10} + \frac{56}{9} \, a^{5} b^{3} x^{9} + \frac{35}{4} \, a^{4} b^{4} x^{8} + 8 \, a^{3} b^{5} x^{7} + \frac{14}{3} \, a^{2} b^{6} x^{6} + \frac{8}{5} \, a b^{7} x^{5} + \frac{1}{4} \, b^{8} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8*x^11,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.154703, size = 105, normalized size = 1.64 \[ \frac{a^{8} x^{12}}{12} + \frac{8 a^{7} b x^{11}}{11} + \frac{14 a^{6} b^{2} x^{10}}{5} + \frac{56 a^{5} b^{3} x^{9}}{9} + \frac{35 a^{4} b^{4} x^{8}}{4} + 8 a^{3} b^{5} x^{7} + \frac{14 a^{2} b^{6} x^{6}}{3} + \frac{8 a b^{7} x^{5}}{5} + \frac{b^{8} x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**8*x**11,x)
[Out]
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GIAC/XCAS [A] time = 0.221758, size = 122, normalized size = 1.91 \[ \frac{1}{12} \, a^{8} x^{12} + \frac{8}{11} \, a^{7} b x^{11} + \frac{14}{5} \, a^{6} b^{2} x^{10} + \frac{56}{9} \, a^{5} b^{3} x^{9} + \frac{35}{4} \, a^{4} b^{4} x^{8} + 8 \, a^{3} b^{5} x^{7} + \frac{14}{3} \, a^{2} b^{6} x^{6} + \frac{8}{5} \, a b^{7} x^{5} + \frac{1}{4} \, b^{8} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8*x^11,x, algorithm="giac")
[Out]