3.610 \(\int \frac{(1+x) \left (1+2 x+x^2\right )^5}{x^{11}} \, dx\)

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]

-1/(10*x^10) - 11/(9*x^9) - 55/(8*x^8) - 165/(7*x^7) - 55/x^6 - 462/(5*x^5) - 23
1/(2*x^4) - 110/x^3 - 165/(2*x^2) - 55/x + x + 11*Log[x]

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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]

-1/(10*x^10) - 11/(9*x^9) - 55/(8*x^8) - 165/(7*x^7) - 55/x^6 - 462/(5*x^5) - 23
1/(2*x^4) - 110/x^3 - 165/(2*x^2) - 55/x + x + 11*Log[x]

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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]

x + 11*log(x) - 55/x - 165/(2*x**2) - 110/x**3 - 231/(2*x**4) - 462/(5*x**5) - 5
5/x**6 - 165/(7*x**7) - 55/(8*x**8) - 11/(9*x**9) - 1/(10*x**10)

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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]

-1/(10*x^10) - 11/(9*x^9) - 55/(8*x^8) - 165/(7*x^7) - 55/x^6 - 462/(5*x^5) - 23
1/(2*x^4) - 110/x^3 - 165/(2*x^2) - 55/x + x + 11*Log[x]

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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]

-1/10/x^10-11/9/x^9-55/8/x^8-165/7/x^7-55/x^6-462/5/x^5-231/2/x^4-110/x^3-165/2/
x^2-55/x+x+11*ln(x)

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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]

x - 1/2520*(138600*x^9 + 207900*x^8 + 277200*x^7 + 291060*x^6 + 232848*x^5 + 138
600*x^4 + 59400*x^3 + 17325*x^2 + 3080*x + 252)/x^10 + 11*log(x)

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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]

1/2520*(2520*x^11 + 27720*x^10*log(x) - 138600*x^9 - 207900*x^8 - 277200*x^7 - 2
91060*x^6 - 232848*x^5 - 138600*x^4 - 59400*x^3 - 17325*x^2 - 3080*x - 252)/x^10

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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]

x + 11*log(x) - (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)

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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]

x - 1/2520*(138600*x^9 + 207900*x^8 + 277200*x^7 + 291060*x^6 + 232848*x^5 + 138
600*x^4 + 59400*x^3 + 17325*x^2 + 3080*x + 252)/x^10 + 11*ln(abs(x))