Optimal. Leaf size=47 \[ \frac{b^2 (a x+b)^9}{9 a^3}+\frac{(a x+b)^{11}}{11 a^3}-\frac{b (a x+b)^{10}}{5 a^3} \]
[Out]
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Rubi [A] time = 0.0775207, antiderivative size = 47, 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 \[ \frac{b^2 (a x+b)^9}{9 a^3}+\frac{(a x+b)^{11}}{11 a^3}-\frac{b (a x+b)^{10}}{5 a^3} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^8*x^10,x]
[Out]
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Rubi in Sympy [A] time = 15.093, size = 39, normalized size = 0.83 \[ \frac{b^{2} \left (a x + b\right )^{9}}{9 a^{3}} - \frac{b \left (a x + b\right )^{10}}{5 a^{3}} + \frac{\left (a x + b\right )^{11}}{11 a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**8*x**10,x)
[Out]
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Mathematica [B] time = 0.00453768, size = 102, normalized size = 2.17 \[ \frac{a^8 x^{11}}{11}+\frac{4}{5} a^7 b x^{10}+\frac{28}{9} a^6 b^2 x^9+7 a^5 b^3 x^8+10 a^4 b^4 x^7+\frac{28}{3} a^3 b^5 x^6+\frac{28}{5} a^2 b^6 x^5+2 a b^7 x^4+\frac{b^8 x^3}{3} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^8*x^10,x]
[Out]
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Maple [B] time = 0.002, size = 91, normalized size = 1.9 \[{\frac{{a}^{8}{x}^{11}}{11}}+{\frac{4\,{a}^{7}b{x}^{10}}{5}}+{\frac{28\,{a}^{6}{b}^{2}{x}^{9}}{9}}+7\,{a}^{5}{b}^{3}{x}^{8}+10\,{a}^{4}{b}^{4}{x}^{7}+{\frac{28\,{a}^{3}{b}^{5}{x}^{6}}{3}}+{\frac{28\,{a}^{2}{b}^{6}{x}^{5}}{5}}+2\,a{b}^{7}{x}^{4}+{\frac{{b}^{8}{x}^{3}}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^8*x^10,x)
[Out]
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Maxima [A] time = 1.42572, size = 122, normalized size = 2.6 \[ \frac{1}{11} \, a^{8} x^{11} + \frac{4}{5} \, a^{7} b x^{10} + \frac{28}{9} \, a^{6} b^{2} x^{9} + 7 \, a^{5} b^{3} x^{8} + 10 \, a^{4} b^{4} x^{7} + \frac{28}{3} \, a^{3} b^{5} x^{6} + \frac{28}{5} \, a^{2} b^{6} x^{5} + 2 \, a b^{7} x^{4} + \frac{1}{3} \, b^{8} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8*x^10,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211172, size = 122, normalized size = 2.6 \[ \frac{1}{11} \, a^{8} x^{11} + \frac{4}{5} \, a^{7} b x^{10} + \frac{28}{9} \, a^{6} b^{2} x^{9} + 7 \, a^{5} b^{3} x^{8} + 10 \, a^{4} b^{4} x^{7} + \frac{28}{3} \, a^{3} b^{5} x^{6} + \frac{28}{5} \, a^{2} b^{6} x^{5} + 2 \, a b^{7} x^{4} + \frac{1}{3} \, b^{8} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8*x^10,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.149122, size = 102, normalized size = 2.17 \[ \frac{a^{8} x^{11}}{11} + \frac{4 a^{7} b x^{10}}{5} + \frac{28 a^{6} b^{2} x^{9}}{9} + 7 a^{5} b^{3} x^{8} + 10 a^{4} b^{4} x^{7} + \frac{28 a^{3} b^{5} x^{6}}{3} + \frac{28 a^{2} b^{6} x^{5}}{5} + 2 a b^{7} x^{4} + \frac{b^{8} x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**8*x**10,x)
[Out]
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GIAC/XCAS [A] time = 0.227563, size = 122, normalized size = 2.6 \[ \frac{1}{11} \, a^{8} x^{11} + \frac{4}{5} \, a^{7} b x^{10} + \frac{28}{9} \, a^{6} b^{2} x^{9} + 7 \, a^{5} b^{3} x^{8} + 10 \, a^{4} b^{4} x^{7} + \frac{28}{3} \, a^{3} b^{5} x^{6} + \frac{28}{5} \, a^{2} b^{6} x^{5} + 2 \, a b^{7} x^{4} + \frac{1}{3} \, b^{8} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8*x^10,x, algorithm="giac")
[Out]