3.613 \(\int \frac{(1+x) \left (1+2 x+x^2\right )^5}{x^{14}} \, dx\)

Optimal. Leaf size=25 \[ \frac{(x+1)^{12}}{156 x^{12}}-\frac{(x+1)^{12}}{13 x^{13}} \]

[Out]

-(1 + x)^12/(13*x^13) + (1 + x)^12/(156*x^12)

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Rubi [A]  time = 0.0166529, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.176 \[ \frac{(x+1)^{12}}{156 x^{12}}-\frac{(x+1)^{12}}{13 x^{13}} \]

Antiderivative was successfully verified.

[In]  Int[((1 + x)*(1 + 2*x + x^2)^5)/x^14,x]

[Out]

-(1 + x)^12/(13*x^13) + (1 + x)^12/(156*x^12)

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Rubi in Sympy [A]  time = 5.39758, size = 19, normalized size = 0.76 \[ \frac{\left (x + 1\right )^{12}}{156 x^{12}} - \frac{\left (x + 1\right )^{12}}{13 x^{13}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1+x)*(x**2+2*x+1)**5/x**14,x)

[Out]

(x + 1)**12/(156*x**12) - (x + 1)**12/(13*x**13)

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Mathematica [B]  time = 0.00433001, size = 77, normalized size = 3.08 \[ -\frac{1}{13 x^{13}}-\frac{11}{12 x^{12}}-\frac{5}{x^{11}}-\frac{33}{2 x^{10}}-\frac{110}{3 x^9}-\frac{231}{4 x^8}-\frac{66}{x^7}-\frac{55}{x^6}-\frac{33}{x^5}-\frac{55}{4 x^4}-\frac{11}{3 x^3}-\frac{1}{2 x^2} \]

Antiderivative was successfully verified.

[In]  Integrate[((1 + x)*(1 + 2*x + x^2)^5)/x^14,x]

[Out]

-1/(13*x^13) - 11/(12*x^12) - 5/x^11 - 33/(2*x^10) - 110/(3*x^9) - 231/(4*x^8) -
66/x^7 - 55/x^6 - 33/x^5 - 55/(4*x^4) - 11/(3*x^3) - 1/(2*x^2)

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Maple [B]  time = 0.009, size = 62, normalized size = 2.5 \[ -{\frac{11}{12\,{x}^{12}}}-{\frac{1}{13\,{x}^{13}}}-55\,{x}^{-6}-{\frac{55}{4\,{x}^{4}}}-{\frac{33}{2\,{x}^{10}}}-{\frac{231}{4\,{x}^{8}}}-5\,{x}^{-11}-{\frac{110}{3\,{x}^{9}}}-{\frac{11}{3\,{x}^{3}}}-{\frac{1}{2\,{x}^{2}}}-33\,{x}^{-5}-66\,{x}^{-7} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1+x)*(x^2+2*x+1)^5/x^14,x)

[Out]

-11/12/x^12-1/13/x^13-55/x^6-55/4/x^4-33/2/x^10-231/4/x^8-5/x^11-110/3/x^9-11/3/
x^3-1/2/x^2-33/x^5-66/x^7

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Maxima [A]  time = 0.684143, size = 81, normalized size = 3.24 \[ -\frac{78 \, x^{11} + 572 \, x^{10} + 2145 \, x^{9} + 5148 \, x^{8} + 8580 \, x^{7} + 10296 \, x^{6} + 9009 \, x^{5} + 5720 \, x^{4} + 2574 \, x^{3} + 780 \, x^{2} + 143 \, x + 12}{156 \, x^{13}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 + 2*x + 1)^5*(x + 1)/x^14,x, algorithm="maxima")

[Out]

-1/156*(78*x^11 + 572*x^10 + 2145*x^9 + 5148*x^8 + 8580*x^7 + 10296*x^6 + 9009*x
^5 + 5720*x^4 + 2574*x^3 + 780*x^2 + 143*x + 12)/x^13

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Fricas [A]  time = 0.260617, size = 81, normalized size = 3.24 \[ -\frac{78 \, x^{11} + 572 \, x^{10} + 2145 \, x^{9} + 5148 \, x^{8} + 8580 \, x^{7} + 10296 \, x^{6} + 9009 \, x^{5} + 5720 \, x^{4} + 2574 \, x^{3} + 780 \, x^{2} + 143 \, x + 12}{156 \, x^{13}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 + 2*x + 1)^5*(x + 1)/x^14,x, algorithm="fricas")

[Out]

-1/156*(78*x^11 + 572*x^10 + 2145*x^9 + 5148*x^8 + 8580*x^7 + 10296*x^6 + 9009*x
^5 + 5720*x^4 + 2574*x^3 + 780*x^2 + 143*x + 12)/x^13

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Sympy [A]  time = 0.53183, size = 61, normalized size = 2.44 \[ - \frac{78 x^{11} + 572 x^{10} + 2145 x^{9} + 5148 x^{8} + 8580 x^{7} + 10296 x^{6} + 9009 x^{5} + 5720 x^{4} + 2574 x^{3} + 780 x^{2} + 143 x + 12}{156 x^{13}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1+x)*(x**2+2*x+1)**5/x**14,x)

[Out]

-(78*x**11 + 572*x**10 + 2145*x**9 + 5148*x**8 + 8580*x**7 + 10296*x**6 + 9009*x
**5 + 5720*x**4 + 2574*x**3 + 780*x**2 + 143*x + 12)/(156*x**13)

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GIAC/XCAS [A]  time = 0.266614, size = 81, normalized size = 3.24 \[ -\frac{78 \, x^{11} + 572 \, x^{10} + 2145 \, x^{9} + 5148 \, x^{8} + 8580 \, x^{7} + 10296 \, x^{6} + 9009 \, x^{5} + 5720 \, x^{4} + 2574 \, x^{3} + 780 \, x^{2} + 143 \, x + 12}{156 \, x^{13}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 + 2*x + 1)^5*(x + 1)/x^14,x, algorithm="giac")

[Out]

-1/156*(78*x^11 + 572*x^10 + 2145*x^9 + 5148*x^8 + 8580*x^7 + 10296*x^6 + 9009*x
^5 + 5720*x^4 + 2574*x^3 + 780*x^2 + 143*x + 12)/x^13