Optimal. Leaf size=70 \[ -\frac{1}{10 x^{10}}-\frac{11}{9 x^9}-\frac{55}{8 x^8}-\frac{165}{7 x^7}-\frac{55}{x^6}-\frac{462}{5 x^5}-\frac{231}{2 x^4}-\frac{110}{x^3}-\frac{165}{2 x^2}+x-\frac{55}{x}+11 \log (x) \]
[Out]
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Rubi [A] time = 0.0475012, antiderivative size = 70, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ -\frac{1}{10 x^{10}}-\frac{11}{9 x^9}-\frac{55}{8 x^8}-\frac{165}{7 x^7}-\frac{55}{x^6}-\frac{462}{5 x^5}-\frac{231}{2 x^4}-\frac{110}{x^3}-\frac{165}{2 x^2}+x-\frac{55}{x}+11 \log (x) \]
Antiderivative was successfully verified.
[In] Int[((1 + x)*(1 + 2*x + x^2)^5)/x^11,x]
[Out]
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Rubi in Sympy [A] time = 9.49998, size = 66, normalized size = 0.94 \[ x + 11 \log{\left (x \right )} - \frac{55}{x} - \frac{165}{2 x^{2}} - \frac{110}{x^{3}} - \frac{231}{2 x^{4}} - \frac{462}{5 x^{5}} - \frac{55}{x^{6}} - \frac{165}{7 x^{7}} - \frac{55}{8 x^{8}} - \frac{11}{9 x^{9}} - \frac{1}{10 x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x)*(x**2+2*x+1)**5/x**11,x)
[Out]
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Mathematica [A] time = 0.00577121, size = 70, normalized size = 1. \[ -\frac{1}{10 x^{10}}-\frac{11}{9 x^9}-\frac{55}{8 x^8}-\frac{165}{7 x^7}-\frac{55}{x^6}-\frac{462}{5 x^5}-\frac{231}{2 x^4}-\frac{110}{x^3}-\frac{165}{2 x^2}+x-\frac{55}{x}+11 \log (x) \]
Antiderivative was successfully verified.
[In] Integrate[((1 + x)*(1 + 2*x + x^2)^5)/x^11,x]
[Out]
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Maple [A] time = 0.01, size = 57, normalized size = 0.8 \[ -{\frac{1}{10\,{x}^{10}}}-{\frac{11}{9\,{x}^{9}}}-{\frac{55}{8\,{x}^{8}}}-{\frac{165}{7\,{x}^{7}}}-55\,{x}^{-6}-{\frac{462}{5\,{x}^{5}}}-{\frac{231}{2\,{x}^{4}}}-110\,{x}^{-3}-{\frac{165}{2\,{x}^{2}}}-55\,{x}^{-1}+x+11\,\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x)*(x^2+2*x+1)^5/x^11,x)
[Out]
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Maxima [A] time = 0.68705, size = 76, normalized size = 1.09 \[ x - \frac{138600 \, x^{9} + 207900 \, x^{8} + 277200 \, x^{7} + 291060 \, x^{6} + 232848 \, x^{5} + 138600 \, x^{4} + 59400 \, x^{3} + 17325 \, x^{2} + 3080 \, x + 252}{2520 \, x^{10}} + 11 \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 1)^5*(x + 1)/x^11,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.309999, size = 84, normalized size = 1.2 \[ \frac{2520 \, x^{11} + 27720 \, x^{10} \log \left (x\right ) - 138600 \, x^{9} - 207900 \, x^{8} - 277200 \, x^{7} - 291060 \, x^{6} - 232848 \, x^{5} - 138600 \, x^{4} - 59400 \, x^{3} - 17325 \, x^{2} - 3080 \, x - 252}{2520 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 1)^5*(x + 1)/x^11,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.463826, size = 56, normalized size = 0.8 \[ x + 11 \log{\left (x \right )} - \frac{138600 x^{9} + 207900 x^{8} + 277200 x^{7} + 291060 x^{6} + 232848 x^{5} + 138600 x^{4} + 59400 x^{3} + 17325 x^{2} + 3080 x + 252}{2520 x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1+x)*(x**2+2*x+1)**5/x**11,x)
[Out]
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GIAC/XCAS [A] time = 0.267507, size = 77, normalized size = 1.1 \[ x - \frac{138600 \, x^{9} + 207900 \, x^{8} + 277200 \, x^{7} + 291060 \, x^{6} + 232848 \, x^{5} + 138600 \, x^{4} + 59400 \, x^{3} + 17325 \, x^{2} + 3080 \, x + 252}{2520 \, x^{10}} + 11 \,{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 1)^5*(x + 1)/x^11,x, algorithm="giac")
[Out]