Optimal. Leaf size=30 \[ \frac{(a x+b)^{10}}{10 a^2}-\frac{b (a x+b)^9}{9 a^2} \]
[Out]
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Rubi [A] time = 0.042959, antiderivative size = 30, 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 \[ \frac{(a x+b)^{10}}{10 a^2}-\frac{b (a x+b)^9}{9 a^2} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^8*x^9,x]
[Out]
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Rubi in Sympy [A] time = 12.1946, size = 24, normalized size = 0.8 \[ - \frac{b \left (a x + b\right )^{9}}{9 a^{2}} + \frac{\left (a x + b\right )^{10}}{10 a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**8*x**9,x)
[Out]
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Mathematica [B] time = 0.00431785, size = 104, normalized size = 3.47 \[ \frac{a^8 x^{10}}{10}+\frac{8}{9} a^7 b x^9+\frac{7}{2} a^6 b^2 x^8+8 a^5 b^3 x^7+\frac{35}{3} a^4 b^4 x^6+\frac{56}{5} a^3 b^5 x^5+7 a^2 b^6 x^4+\frac{8}{3} a b^7 x^3+\frac{b^8 x^2}{2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^8*x^9,x]
[Out]
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Maple [B] time = 0.002, size = 91, normalized size = 3. \[{\frac{{a}^{8}{x}^{10}}{10}}+{\frac{8\,{a}^{7}b{x}^{9}}{9}}+{\frac{7\,{a}^{6}{b}^{2}{x}^{8}}{2}}+8\,{a}^{5}{b}^{3}{x}^{7}+{\frac{35\,{a}^{4}{b}^{4}{x}^{6}}{3}}+{\frac{56\,{a}^{3}{b}^{5}{x}^{5}}{5}}+7\,{a}^{2}{b}^{6}{x}^{4}+{\frac{8\,a{b}^{7}{x}^{3}}{3}}+{\frac{{x}^{2}{b}^{8}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^8*x^9,x)
[Out]
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Maxima [A] time = 1.44819, size = 122, normalized size = 4.07 \[ \frac{1}{10} \, a^{8} x^{10} + \frac{8}{9} \, a^{7} b x^{9} + \frac{7}{2} \, a^{6} b^{2} x^{8} + 8 \, a^{5} b^{3} x^{7} + \frac{35}{3} \, a^{4} b^{4} x^{6} + \frac{56}{5} \, a^{3} b^{5} x^{5} + 7 \, a^{2} b^{6} x^{4} + \frac{8}{3} \, a b^{7} x^{3} + \frac{1}{2} \, b^{8} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8*x^9,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211513, size = 122, normalized size = 4.07 \[ \frac{1}{10} \, a^{8} x^{10} + \frac{8}{9} \, a^{7} b x^{9} + \frac{7}{2} \, a^{6} b^{2} x^{8} + 8 \, a^{5} b^{3} x^{7} + \frac{35}{3} \, a^{4} b^{4} x^{6} + \frac{56}{5} \, a^{3} b^{5} x^{5} + 7 \, a^{2} b^{6} x^{4} + \frac{8}{3} \, a b^{7} x^{3} + \frac{1}{2} \, b^{8} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8*x^9,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.1548, size = 104, normalized size = 3.47 \[ \frac{a^{8} x^{10}}{10} + \frac{8 a^{7} b x^{9}}{9} + \frac{7 a^{6} b^{2} x^{8}}{2} + 8 a^{5} b^{3} x^{7} + \frac{35 a^{4} b^{4} x^{6}}{3} + \frac{56 a^{3} b^{5} x^{5}}{5} + 7 a^{2} b^{6} x^{4} + \frac{8 a b^{7} x^{3}}{3} + \frac{b^{8} x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**8*x**9,x)
[Out]
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GIAC/XCAS [A] time = 0.221456, size = 122, normalized size = 4.07 \[ \frac{1}{10} \, a^{8} x^{10} + \frac{8}{9} \, a^{7} b x^{9} + \frac{7}{2} \, a^{6} b^{2} x^{8} + 8 \, a^{5} b^{3} x^{7} + \frac{35}{3} \, a^{4} b^{4} x^{6} + \frac{56}{5} \, a^{3} b^{5} x^{5} + 7 \, a^{2} b^{6} x^{4} + \frac{8}{3} \, a b^{7} x^{3} + \frac{1}{2} \, b^{8} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8*x^9,x, algorithm="giac")
[Out]