Optimal. Leaf size=132 \[ -\frac{a^{11}}{9 x^9}-\frac{11 a^{10} b}{8 x^8}-\frac{55 a^9 b^2}{7 x^7}-\frac{55 a^8 b^3}{2 x^6}-\frac{66 a^7 b^4}{x^5}-\frac{231 a^6 b^5}{2 x^4}-\frac{154 a^5 b^6}{x^3}-\frac{165 a^4 b^7}{x^2}-\frac{165 a^3 b^8}{x}+55 a^2 b^9 \log (x)+11 a b^{10} x+\frac{b^{11} x^2}{2} \]
[Out]
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Rubi [A] time = 0.146417, antiderivative size = 132, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ -\frac{a^{11}}{9 x^9}-\frac{11 a^{10} b}{8 x^8}-\frac{55 a^9 b^2}{7 x^7}-\frac{55 a^8 b^3}{2 x^6}-\frac{66 a^7 b^4}{x^5}-\frac{231 a^6 b^5}{2 x^4}-\frac{154 a^5 b^6}{x^3}-\frac{165 a^4 b^7}{x^2}-\frac{165 a^3 b^8}{x}+55 a^2 b^9 \log (x)+11 a b^{10} x+\frac{b^{11} x^2}{2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^11/x^10,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{11}}{9 x^{9}} - \frac{11 a^{10} b}{8 x^{8}} - \frac{55 a^{9} b^{2}}{7 x^{7}} - \frac{55 a^{8} b^{3}}{2 x^{6}} - \frac{66 a^{7} b^{4}}{x^{5}} - \frac{231 a^{6} b^{5}}{2 x^{4}} - \frac{154 a^{5} b^{6}}{x^{3}} - \frac{165 a^{4} b^{7}}{x^{2}} - \frac{165 a^{3} b^{8}}{x} + 55 a^{2} b^{9} \log{\left (x \right )} + 11 a b^{10} x + b^{11} \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**11/x**10,x)
[Out]
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Mathematica [A] time = 0.00778839, size = 132, normalized size = 1. \[ -\frac{a^{11}}{9 x^9}-\frac{11 a^{10} b}{8 x^8}-\frac{55 a^9 b^2}{7 x^7}-\frac{55 a^8 b^3}{2 x^6}-\frac{66 a^7 b^4}{x^5}-\frac{231 a^6 b^5}{2 x^4}-\frac{154 a^5 b^6}{x^3}-\frac{165 a^4 b^7}{x^2}-\frac{165 a^3 b^8}{x}+55 a^2 b^9 \log (x)+11 a b^{10} x+\frac{b^{11} x^2}{2} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^11/x^10,x]
[Out]
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Maple [A] time = 0.016, size = 121, normalized size = 0.9 \[ -{\frac{{a}^{11}}{9\,{x}^{9}}}-{\frac{11\,{a}^{10}b}{8\,{x}^{8}}}-{\frac{55\,{a}^{9}{b}^{2}}{7\,{x}^{7}}}-{\frac{55\,{a}^{8}{b}^{3}}{2\,{x}^{6}}}-66\,{\frac{{a}^{7}{b}^{4}}{{x}^{5}}}-{\frac{231\,{a}^{6}{b}^{5}}{2\,{x}^{4}}}-154\,{\frac{{a}^{5}{b}^{6}}{{x}^{3}}}-165\,{\frac{{a}^{4}{b}^{7}}{{x}^{2}}}-165\,{\frac{{a}^{3}{b}^{8}}{x}}+11\,a{b}^{10}x+{\frac{{b}^{11}{x}^{2}}{2}}+55\,{a}^{2}{b}^{9}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^11/x^10,x)
[Out]
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Maxima [A] time = 1.34993, size = 163, normalized size = 1.23 \[ \frac{1}{2} \, b^{11} x^{2} + 11 \, a b^{10} x + 55 \, a^{2} b^{9} \log \left (x\right ) - \frac{83160 \, a^{3} b^{8} x^{8} + 83160 \, a^{4} b^{7} x^{7} + 77616 \, a^{5} b^{6} x^{6} + 58212 \, a^{6} b^{5} x^{5} + 33264 \, a^{7} b^{4} x^{4} + 13860 \, a^{8} b^{3} x^{3} + 3960 \, a^{9} b^{2} x^{2} + 693 \, a^{10} b x + 56 \, a^{11}}{504 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^11/x^10,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211931, size = 169, normalized size = 1.28 \[ \frac{252 \, b^{11} x^{11} + 5544 \, a b^{10} x^{10} + 27720 \, a^{2} b^{9} x^{9} \log \left (x\right ) - 83160 \, a^{3} b^{8} x^{8} - 83160 \, a^{4} b^{7} x^{7} - 77616 \, a^{5} b^{6} x^{6} - 58212 \, a^{6} b^{5} x^{5} - 33264 \, a^{7} b^{4} x^{4} - 13860 \, a^{8} b^{3} x^{3} - 3960 \, a^{9} b^{2} x^{2} - 693 \, a^{10} b x - 56 \, a^{11}}{504 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^11/x^10,x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.41833, size = 129, normalized size = 0.98 \[ 55 a^{2} b^{9} \log{\left (x \right )} + 11 a b^{10} x + \frac{b^{11} x^{2}}{2} - \frac{56 a^{11} + 693 a^{10} b x + 3960 a^{9} b^{2} x^{2} + 13860 a^{8} b^{3} x^{3} + 33264 a^{7} b^{4} x^{4} + 58212 a^{6} b^{5} x^{5} + 77616 a^{5} b^{6} x^{6} + 83160 a^{4} b^{7} x^{7} + 83160 a^{3} b^{8} x^{8}}{504 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**11/x**10,x)
[Out]
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GIAC/XCAS [A] time = 0.204582, size = 165, normalized size = 1.25 \[ \frac{1}{2} \, b^{11} x^{2} + 11 \, a b^{10} x + 55 \, a^{2} b^{9}{\rm ln}\left ({\left | x \right |}\right ) - \frac{83160 \, a^{3} b^{8} x^{8} + 83160 \, a^{4} b^{7} x^{7} + 77616 \, a^{5} b^{6} x^{6} + 58212 \, a^{6} b^{5} x^{5} + 33264 \, a^{7} b^{4} x^{4} + 13860 \, a^{8} b^{3} x^{3} + 3960 \, a^{9} b^{2} x^{2} + 693 \, a^{10} b x + 56 \, a^{11}}{504 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^11/x^10,x, algorithm="giac")
[Out]