Optimal. Leaf size=106 \[ \frac{a^8 x^{16}}{16}+\frac{8}{15} a^7 b x^{15}+2 a^6 b^2 x^{14}+\frac{56}{13} a^5 b^3 x^{13}+\frac{35}{6} a^4 b^4 x^{12}+\frac{56}{11} a^3 b^5 x^{11}+\frac{14}{5} a^2 b^6 x^{10}+\frac{8}{9} a b^7 x^9+\frac{b^8 x^8}{8} \]
[Out]
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Rubi [A] time = 0.128805, antiderivative size = 106, 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 \[ \frac{a^8 x^{16}}{16}+\frac{8}{15} a^7 b x^{15}+2 a^6 b^2 x^{14}+\frac{56}{13} a^5 b^3 x^{13}+\frac{35}{6} a^4 b^4 x^{12}+\frac{56}{11} a^3 b^5 x^{11}+\frac{14}{5} a^2 b^6 x^{10}+\frac{8}{9} a b^7 x^9+\frac{b^8 x^8}{8} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^8*x^15,x]
[Out]
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Rubi in Sympy [A] time = 23.0785, size = 105, normalized size = 0.99 \[ \frac{a^{8} x^{16}}{16} + \frac{8 a^{7} b x^{15}}{15} + 2 a^{6} b^{2} x^{14} + \frac{56 a^{5} b^{3} x^{13}}{13} + \frac{35 a^{4} b^{4} x^{12}}{6} + \frac{56 a^{3} b^{5} x^{11}}{11} + \frac{14 a^{2} b^{6} x^{10}}{5} + \frac{8 a b^{7} x^{9}}{9} + \frac{b^{8} x^{8}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**8*x**15,x)
[Out]
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Mathematica [A] time = 0.00453576, size = 106, normalized size = 1. \[ \frac{a^8 x^{16}}{16}+\frac{8}{15} a^7 b x^{15}+2 a^6 b^2 x^{14}+\frac{56}{13} a^5 b^3 x^{13}+\frac{35}{6} a^4 b^4 x^{12}+\frac{56}{11} a^3 b^5 x^{11}+\frac{14}{5} a^2 b^6 x^{10}+\frac{8}{9} a b^7 x^9+\frac{b^8 x^8}{8} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^8*x^15,x]
[Out]
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Maple [A] time = 0.002, size = 91, normalized size = 0.9 \[{\frac{{b}^{8}{x}^{8}}{8}}+{\frac{8\,a{b}^{7}{x}^{9}}{9}}+{\frac{14\,{a}^{2}{b}^{6}{x}^{10}}{5}}+{\frac{56\,{a}^{3}{b}^{5}{x}^{11}}{11}}+{\frac{35\,{a}^{4}{b}^{4}{x}^{12}}{6}}+{\frac{56\,{a}^{5}{b}^{3}{x}^{13}}{13}}+2\,{a}^{6}{b}^{2}{x}^{14}+{\frac{8\,{a}^{7}b{x}^{15}}{15}}+{\frac{{a}^{8}{x}^{16}}{16}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^8*x^15,x)
[Out]
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Maxima [A] time = 1.43794, size = 122, normalized size = 1.15 \[ \frac{1}{16} \, a^{8} x^{16} + \frac{8}{15} \, a^{7} b x^{15} + 2 \, a^{6} b^{2} x^{14} + \frac{56}{13} \, a^{5} b^{3} x^{13} + \frac{35}{6} \, a^{4} b^{4} x^{12} + \frac{56}{11} \, a^{3} b^{5} x^{11} + \frac{14}{5} \, a^{2} b^{6} x^{10} + \frac{8}{9} \, a b^{7} x^{9} + \frac{1}{8} \, b^{8} x^{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8*x^15,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211693, size = 122, normalized size = 1.15 \[ \frac{1}{16} \, a^{8} x^{16} + \frac{8}{15} \, a^{7} b x^{15} + 2 \, a^{6} b^{2} x^{14} + \frac{56}{13} \, a^{5} b^{3} x^{13} + \frac{35}{6} \, a^{4} b^{4} x^{12} + \frac{56}{11} \, a^{3} b^{5} x^{11} + \frac{14}{5} \, a^{2} b^{6} x^{10} + \frac{8}{9} \, a b^{7} x^{9} + \frac{1}{8} \, b^{8} x^{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8*x^15,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.169245, size = 105, normalized size = 0.99 \[ \frac{a^{8} x^{16}}{16} + \frac{8 a^{7} b x^{15}}{15} + 2 a^{6} b^{2} x^{14} + \frac{56 a^{5} b^{3} x^{13}}{13} + \frac{35 a^{4} b^{4} x^{12}}{6} + \frac{56 a^{3} b^{5} x^{11}}{11} + \frac{14 a^{2} b^{6} x^{10}}{5} + \frac{8 a b^{7} x^{9}}{9} + \frac{b^{8} x^{8}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**8*x**15,x)
[Out]
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GIAC/XCAS [A] time = 0.218988, size = 122, normalized size = 1.15 \[ \frac{1}{16} \, a^{8} x^{16} + \frac{8}{15} \, a^{7} b x^{15} + 2 \, a^{6} b^{2} x^{14} + \frac{56}{13} \, a^{5} b^{3} x^{13} + \frac{35}{6} \, a^{4} b^{4} x^{12} + \frac{56}{11} \, a^{3} b^{5} x^{11} + \frac{14}{5} \, a^{2} b^{6} x^{10} + \frac{8}{9} \, a b^{7} x^{9} + \frac{1}{8} \, b^{8} x^{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8*x^15,x, algorithm="giac")
[Out]