3.621 \(\int \frac{(1+x) \left (1+2 x+x^2\right )^5}{x^{22}} \, dx\)

Optimal. Leaf size=83 \[ -\frac{1}{21 x^{21}}-\frac{11}{20 x^{20}}-\frac{55}{19 x^{19}}-\frac{55}{6 x^{18}}-\frac{330}{17 x^{17}}-\frac{231}{8 x^{16}}-\frac{154}{5 x^{15}}-\frac{165}{7 x^{14}}-\frac{165}{13 x^{13}}-\frac{55}{12 x^{12}}-\frac{1}{x^{11}}-\frac{1}{10 x^{10}} \]

[Out]

-1/(21*x^21) - 11/(20*x^20) - 55/(19*x^19) - 55/(6*x^18) - 330/(17*x^17) - 231/(
8*x^16) - 154/(5*x^15) - 165/(7*x^14) - 165/(13*x^13) - 55/(12*x^12) - x^(-11) -
 1/(10*x^10)

_______________________________________________________________________________________

Rubi [A]  time = 0.0517928, antiderivative size = 83, 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 \[ -\frac{1}{21 x^{21}}-\frac{11}{20 x^{20}}-\frac{55}{19 x^{19}}-\frac{55}{6 x^{18}}-\frac{330}{17 x^{17}}-\frac{231}{8 x^{16}}-\frac{154}{5 x^{15}}-\frac{165}{7 x^{14}}-\frac{165}{13 x^{13}}-\frac{55}{12 x^{12}}-\frac{1}{x^{11}}-\frac{1}{10 x^{10}} \]

Antiderivative was successfully verified.

[In]  Int[((1 + x)*(1 + 2*x + x^2)^5)/x^22,x]

[Out]

-1/(21*x^21) - 11/(20*x^20) - 55/(19*x^19) - 55/(6*x^18) - 330/(17*x^17) - 231/(
8*x^16) - 154/(5*x^15) - 165/(7*x^14) - 165/(13*x^13) - 55/(12*x^12) - x^(-11) -
 1/(10*x^10)

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 11.9796, size = 80, normalized size = 0.96 \[ - \frac{1}{10 x^{10}} - \frac{1}{x^{11}} - \frac{55}{12 x^{12}} - \frac{165}{13 x^{13}} - \frac{165}{7 x^{14}} - \frac{154}{5 x^{15}} - \frac{231}{8 x^{16}} - \frac{330}{17 x^{17}} - \frac{55}{6 x^{18}} - \frac{55}{19 x^{19}} - \frac{11}{20 x^{20}} - \frac{1}{21 x^{21}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1+x)*(x**2+2*x+1)**5/x**22,x)

[Out]

-1/(10*x**10) - 1/x**11 - 55/(12*x**12) - 165/(13*x**13) - 165/(7*x**14) - 154/(
5*x**15) - 231/(8*x**16) - 330/(17*x**17) - 55/(6*x**18) - 55/(19*x**19) - 11/(2
0*x**20) - 1/(21*x**21)

_______________________________________________________________________________________

Mathematica [A]  time = 0.00684348, size = 83, normalized size = 1. \[ -\frac{1}{21 x^{21}}-\frac{11}{20 x^{20}}-\frac{55}{19 x^{19}}-\frac{55}{6 x^{18}}-\frac{330}{17 x^{17}}-\frac{231}{8 x^{16}}-\frac{154}{5 x^{15}}-\frac{165}{7 x^{14}}-\frac{165}{13 x^{13}}-\frac{55}{12 x^{12}}-\frac{1}{x^{11}}-\frac{1}{10 x^{10}} \]

Antiderivative was successfully verified.

[In]  Integrate[((1 + x)*(1 + 2*x + x^2)^5)/x^22,x]

[Out]

-1/(21*x^21) - 11/(20*x^20) - 55/(19*x^19) - 55/(6*x^18) - 330/(17*x^17) - 231/(
8*x^16) - 154/(5*x^15) - 165/(7*x^14) - 165/(13*x^13) - 55/(12*x^12) - x^(-11) -
 1/(10*x^10)

_______________________________________________________________________________________

Maple [A]  time = 0.009, size = 62, normalized size = 0.8 \[ -{\frac{1}{21\,{x}^{21}}}-{\frac{11}{20\,{x}^{20}}}-{\frac{55}{19\,{x}^{19}}}-{\frac{55}{6\,{x}^{18}}}-{\frac{330}{17\,{x}^{17}}}-{\frac{231}{8\,{x}^{16}}}-{\frac{154}{5\,{x}^{15}}}-{\frac{165}{7\,{x}^{14}}}-{\frac{165}{13\,{x}^{13}}}-{\frac{55}{12\,{x}^{12}}}-{x}^{-11}-{\frac{1}{10\,{x}^{10}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1+x)*(x^2+2*x+1)^5/x^22,x)

[Out]

-1/21/x^21-11/20/x^20-55/19/x^19-55/6/x^18-330/17/x^17-231/8/x^16-154/5/x^15-165
/7/x^14-165/13/x^13-55/12/x^12-1/x^11-1/10/x^10

_______________________________________________________________________________________

Maxima [A]  time = 0.692273, size = 81, normalized size = 0.98 \[ -\frac{352716 \, x^{11} + 3527160 \, x^{10} + 16166150 \, x^{9} + 44767800 \, x^{8} + 83140200 \, x^{7} + 108636528 \, x^{6} + 101846745 \, x^{5} + 68468400 \, x^{4} + 32332300 \, x^{3} + 10210200 \, x^{2} + 1939938 \, x + 167960}{3527160 \, x^{21}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 + 2*x + 1)^5*(x + 1)/x^22,x, algorithm="maxima")

[Out]

-1/3527160*(352716*x^11 + 3527160*x^10 + 16166150*x^9 + 44767800*x^8 + 83140200*
x^7 + 108636528*x^6 + 101846745*x^5 + 68468400*x^4 + 32332300*x^3 + 10210200*x^2
 + 1939938*x + 167960)/x^21

_______________________________________________________________________________________

Fricas [A]  time = 0.267598, size = 81, normalized size = 0.98 \[ -\frac{352716 \, x^{11} + 3527160 \, x^{10} + 16166150 \, x^{9} + 44767800 \, x^{8} + 83140200 \, x^{7} + 108636528 \, x^{6} + 101846745 \, x^{5} + 68468400 \, x^{4} + 32332300 \, x^{3} + 10210200 \, x^{2} + 1939938 \, x + 167960}{3527160 \, x^{21}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 + 2*x + 1)^5*(x + 1)/x^22,x, algorithm="fricas")

[Out]

-1/3527160*(352716*x^11 + 3527160*x^10 + 16166150*x^9 + 44767800*x^8 + 83140200*
x^7 + 108636528*x^6 + 101846745*x^5 + 68468400*x^4 + 32332300*x^3 + 10210200*x^2
 + 1939938*x + 167960)/x^21

_______________________________________________________________________________________

Sympy [A]  time = 0.780089, size = 61, normalized size = 0.73 \[ - \frac{352716 x^{11} + 3527160 x^{10} + 16166150 x^{9} + 44767800 x^{8} + 83140200 x^{7} + 108636528 x^{6} + 101846745 x^{5} + 68468400 x^{4} + 32332300 x^{3} + 10210200 x^{2} + 1939938 x + 167960}{3527160 x^{21}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1+x)*(x**2+2*x+1)**5/x**22,x)

[Out]

-(352716*x**11 + 3527160*x**10 + 16166150*x**9 + 44767800*x**8 + 83140200*x**7 +
 108636528*x**6 + 101846745*x**5 + 68468400*x**4 + 32332300*x**3 + 10210200*x**2
 + 1939938*x + 167960)/(3527160*x**21)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.267445, size = 81, normalized size = 0.98 \[ -\frac{352716 \, x^{11} + 3527160 \, x^{10} + 16166150 \, x^{9} + 44767800 \, x^{8} + 83140200 \, x^{7} + 108636528 \, x^{6} + 101846745 \, x^{5} + 68468400 \, x^{4} + 32332300 \, x^{3} + 10210200 \, x^{2} + 1939938 \, x + 167960}{3527160 \, x^{21}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 + 2*x + 1)^5*(x + 1)/x^22,x, algorithm="giac")

[Out]

-1/3527160*(352716*x^11 + 3527160*x^10 + 16166150*x^9 + 44767800*x^8 + 83140200*
x^7 + 108636528*x^6 + 101846745*x^5 + 68468400*x^4 + 32332300*x^3 + 10210200*x^2
 + 1939938*x + 167960)/x^21