Optimal. Leaf size=96 \[ -\frac{a^4 (a x+b)^9}{6435 b^5 x^9}+\frac{a^3 (a x+b)^9}{715 b^4 x^{10}}-\frac{a^2 (a x+b)^9}{143 b^3 x^{11}}+\frac{a (a x+b)^9}{39 b^2 x^{12}}-\frac{(a x+b)^9}{13 b x^{13}} \]
[Out]
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Rubi [A] time = 0.101826, antiderivative size = 96, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ -\frac{a^4 (a x+b)^9}{6435 b^5 x^9}+\frac{a^3 (a x+b)^9}{715 b^4 x^{10}}-\frac{a^2 (a x+b)^9}{143 b^3 x^{11}}+\frac{a (a x+b)^9}{39 b^2 x^{12}}-\frac{(a x+b)^9}{13 b x^{13}} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^8/x^6,x]
[Out]
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Rubi in Sympy [A] time = 20.4684, size = 105, normalized size = 1.09 \[ - \frac{a^{8}}{5 x^{5}} - \frac{4 a^{7} b}{3 x^{6}} - \frac{4 a^{6} b^{2}}{x^{7}} - \frac{7 a^{5} b^{3}}{x^{8}} - \frac{70 a^{4} b^{4}}{9 x^{9}} - \frac{28 a^{3} b^{5}}{5 x^{10}} - \frac{28 a^{2} b^{6}}{11 x^{11}} - \frac{2 a b^{7}}{3 x^{12}} - \frac{b^{8}}{13 x^{13}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**8/x**6,x)
[Out]
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Mathematica [A] time = 0.0155441, size = 104, normalized size = 1.08 \[ -\frac{a^8}{5 x^5}-\frac{4 a^7 b}{3 x^6}-\frac{4 a^6 b^2}{x^7}-\frac{7 a^5 b^3}{x^8}-\frac{70 a^4 b^4}{9 x^9}-\frac{28 a^3 b^5}{5 x^{10}}-\frac{28 a^2 b^6}{11 x^{11}}-\frac{2 a b^7}{3 x^{12}}-\frac{b^8}{13 x^{13}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^8/x^6,x]
[Out]
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Maple [A] time = 0.009, size = 91, normalized size = 1. \[ -{\frac{2\,a{b}^{7}}{3\,{x}^{12}}}-{\frac{{b}^{8}}{13\,{x}^{13}}}-{\frac{4\,{a}^{7}b}{3\,{x}^{6}}}-{\frac{28\,{a}^{3}{b}^{5}}{5\,{x}^{10}}}-7\,{\frac{{a}^{5}{b}^{3}}{{x}^{8}}}-{\frac{28\,{a}^{2}{b}^{6}}{11\,{x}^{11}}}-{\frac{70\,{a}^{4}{b}^{4}}{9\,{x}^{9}}}-{\frac{{a}^{8}}{5\,{x}^{5}}}-4\,{\frac{{a}^{6}{b}^{2}}{{x}^{7}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^8/x^6,x)
[Out]
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Maxima [A] time = 1.45311, size = 122, normalized size = 1.27 \[ -\frac{1287 \, a^{8} x^{8} + 8580 \, a^{7} b x^{7} + 25740 \, a^{6} b^{2} x^{6} + 45045 \, a^{5} b^{3} x^{5} + 50050 \, a^{4} b^{4} x^{4} + 36036 \, a^{3} b^{5} x^{3} + 16380 \, a^{2} b^{6} x^{2} + 4290 \, a b^{7} x + 495 \, b^{8}}{6435 \, x^{13}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8/x^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211146, size = 122, normalized size = 1.27 \[ -\frac{1287 \, a^{8} x^{8} + 8580 \, a^{7} b x^{7} + 25740 \, a^{6} b^{2} x^{6} + 45045 \, a^{5} b^{3} x^{5} + 50050 \, a^{4} b^{4} x^{4} + 36036 \, a^{3} b^{5} x^{3} + 16380 \, a^{2} b^{6} x^{2} + 4290 \, a b^{7} x + 495 \, b^{8}}{6435 \, x^{13}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8/x^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.63455, size = 97, normalized size = 1.01 \[ - \frac{1287 a^{8} x^{8} + 8580 a^{7} b x^{7} + 25740 a^{6} b^{2} x^{6} + 45045 a^{5} b^{3} x^{5} + 50050 a^{4} b^{4} x^{4} + 36036 a^{3} b^{5} x^{3} + 16380 a^{2} b^{6} x^{2} + 4290 a b^{7} x + 495 b^{8}}{6435 x^{13}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**8/x**6,x)
[Out]
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GIAC/XCAS [A] time = 0.221118, size = 122, normalized size = 1.27 \[ -\frac{1287 \, a^{8} x^{8} + 8580 \, a^{7} b x^{7} + 25740 \, a^{6} b^{2} x^{6} + 45045 \, a^{5} b^{3} x^{5} + 50050 \, a^{4} b^{4} x^{4} + 36036 \, a^{3} b^{5} x^{3} + 16380 \, a^{2} b^{6} x^{2} + 4290 \, a b^{7} x + 495 \, b^{8}}{6435 \, x^{13}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8/x^6,x, algorithm="giac")
[Out]