Optimal. Leaf size=81 \[ \frac{b^4 (a x+b)^9}{9 a^5}-\frac{2 b^3 (a x+b)^{10}}{5 a^5}+\frac{6 b^2 (a x+b)^{11}}{11 a^5}+\frac{(a x+b)^{13}}{13 a^5}-\frac{b (a x+b)^{12}}{3 a^5} \]
[Out]
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Rubi [A] time = 0.109553, antiderivative size = 81, 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 \[ \frac{b^4 (a x+b)^9}{9 a^5}-\frac{2 b^3 (a x+b)^{10}}{5 a^5}+\frac{6 b^2 (a x+b)^{11}}{11 a^5}+\frac{(a x+b)^{13}}{13 a^5}-\frac{b (a x+b)^{12}}{3 a^5} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^8*x^12,x]
[Out]
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Rubi in Sympy [A] time = 21.0719, size = 73, normalized size = 0.9 \[ \frac{b^{4} \left (a x + b\right )^{9}}{9 a^{5}} - \frac{2 b^{3} \left (a x + b\right )^{10}}{5 a^{5}} + \frac{6 b^{2} \left (a x + b\right )^{11}}{11 a^{5}} - \frac{b \left (a x + b\right )^{12}}{3 a^{5}} + \frac{\left (a x + b\right )^{13}}{13 a^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**8*x**12,x)
[Out]
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Mathematica [A] time = 0.00551555, size = 104, normalized size = 1.28 \[ \frac{a^8 x^{13}}{13}+\frac{2}{3} a^7 b x^{12}+\frac{28}{11} a^6 b^2 x^{11}+\frac{28}{5} a^5 b^3 x^{10}+\frac{70}{9} a^4 b^4 x^9+7 a^3 b^5 x^8+4 a^2 b^6 x^7+\frac{4}{3} a b^7 x^6+\frac{b^8 x^5}{5} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^8*x^12,x]
[Out]
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Maple [A] time = 0.003, size = 91, normalized size = 1.1 \[{\frac{{a}^{8}{x}^{13}}{13}}+{\frac{2\,{a}^{7}b{x}^{12}}{3}}+{\frac{28\,{a}^{6}{b}^{2}{x}^{11}}{11}}+{\frac{28\,{a}^{5}{b}^{3}{x}^{10}}{5}}+{\frac{70\,{a}^{4}{b}^{4}{x}^{9}}{9}}+7\,{a}^{3}{b}^{5}{x}^{8}+4\,{a}^{2}{b}^{6}{x}^{7}+{\frac{4\,a{b}^{7}{x}^{6}}{3}}+{\frac{{b}^{8}{x}^{5}}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^8*x^12,x)
[Out]
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Maxima [A] time = 1.44445, size = 122, normalized size = 1.51 \[ \frac{1}{13} \, a^{8} x^{13} + \frac{2}{3} \, a^{7} b x^{12} + \frac{28}{11} \, a^{6} b^{2} x^{11} + \frac{28}{5} \, a^{5} b^{3} x^{10} + \frac{70}{9} \, a^{4} b^{4} x^{9} + 7 \, a^{3} b^{5} x^{8} + 4 \, a^{2} b^{6} x^{7} + \frac{4}{3} \, a b^{7} x^{6} + \frac{1}{5} \, b^{8} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8*x^12,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212989, size = 122, normalized size = 1.51 \[ \frac{1}{13} \, a^{8} x^{13} + \frac{2}{3} \, a^{7} b x^{12} + \frac{28}{11} \, a^{6} b^{2} x^{11} + \frac{28}{5} \, a^{5} b^{3} x^{10} + \frac{70}{9} \, a^{4} b^{4} x^{9} + 7 \, a^{3} b^{5} x^{8} + 4 \, a^{2} b^{6} x^{7} + \frac{4}{3} \, a b^{7} x^{6} + \frac{1}{5} \, b^{8} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8*x^12,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.154342, size = 104, normalized size = 1.28 \[ \frac{a^{8} x^{13}}{13} + \frac{2 a^{7} b x^{12}}{3} + \frac{28 a^{6} b^{2} x^{11}}{11} + \frac{28 a^{5} b^{3} x^{10}}{5} + \frac{70 a^{4} b^{4} x^{9}}{9} + 7 a^{3} b^{5} x^{8} + 4 a^{2} b^{6} x^{7} + \frac{4 a b^{7} x^{6}}{3} + \frac{b^{8} x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**8*x**12,x)
[Out]
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GIAC/XCAS [A] time = 0.225425, size = 122, normalized size = 1.51 \[ \frac{1}{13} \, a^{8} x^{13} + \frac{2}{3} \, a^{7} b x^{12} + \frac{28}{11} \, a^{6} b^{2} x^{11} + \frac{28}{5} \, a^{5} b^{3} x^{10} + \frac{70}{9} \, a^{4} b^{4} x^{9} + 7 \, a^{3} b^{5} x^{8} + 4 \, a^{2} b^{6} x^{7} + \frac{4}{3} \, a b^{7} x^{6} + \frac{1}{5} \, b^{8} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8*x^12,x, algorithm="giac")
[Out]