Optimal. Leaf size=70 \[ \frac{x^9}{9}+\frac{11 x^8}{8}+\frac{55 x^7}{7}+\frac{55 x^6}{2}+66 x^5+\frac{231 x^4}{2}+154 x^3+165 x^2-\frac{1}{2 x^2}+165 x-\frac{11}{x}+55 \log (x) \]
[Out]
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Rubi [A] time = 0.0493859, 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 \[ \frac{x^9}{9}+\frac{11 x^8}{8}+\frac{55 x^7}{7}+\frac{55 x^6}{2}+66 x^5+\frac{231 x^4}{2}+154 x^3+165 x^2-\frac{1}{2 x^2}+165 x-\frac{11}{x}+55 \log (x) \]
Antiderivative was successfully verified.
[In] Int[((1 + x)*(1 + 2*x + x^2)^5)/x^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{x^{9}}{9} + \frac{11 x^{8}}{8} + \frac{55 x^{7}}{7} + \frac{55 x^{6}}{2} + 66 x^{5} + \frac{231 x^{4}}{2} + 154 x^{3} + 165 x + 55 \log{\left (x \right )} + 330 \int x\, dx - \frac{11}{x} - \frac{1}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x)*(x**2+2*x+1)**5/x**3,x)
[Out]
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Mathematica [A] time = 0.00450056, size = 70, normalized size = 1. \[ \frac{x^9}{9}+\frac{11 x^8}{8}+\frac{55 x^7}{7}+\frac{55 x^6}{2}+66 x^5+\frac{231 x^4}{2}+154 x^3+165 x^2-\frac{1}{2 x^2}+165 x-\frac{11}{x}+55 \log (x) \]
Antiderivative was successfully verified.
[In] Integrate[((1 + x)*(1 + 2*x + x^2)^5)/x^3,x]
[Out]
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Maple [A] time = 0.008, size = 59, normalized size = 0.8 \[ -{\frac{1}{2\,{x}^{2}}}-11\,{x}^{-1}+165\,x+165\,{x}^{2}+154\,{x}^{3}+{\frac{231\,{x}^{4}}{2}}+66\,{x}^{5}+{\frac{55\,{x}^{6}}{2}}+{\frac{55\,{x}^{7}}{7}}+{\frac{11\,{x}^{8}}{8}}+{\frac{{x}^{9}}{9}}+55\,\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x)*(x^2+2*x+1)^5/x^3,x)
[Out]
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Maxima [A] time = 0.683104, size = 78, normalized size = 1.11 \[ \frac{1}{9} \, x^{9} + \frac{11}{8} \, x^{8} + \frac{55}{7} \, x^{7} + \frac{55}{2} \, x^{6} + 66 \, x^{5} + \frac{231}{2} \, x^{4} + 154 \, x^{3} + 165 \, x^{2} + 165 \, x - \frac{22 \, x + 1}{2 \, x^{2}} + 55 \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 1)^5*(x + 1)/x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.284959, size = 84, normalized size = 1.2 \[ \frac{56 \, x^{11} + 693 \, x^{10} + 3960 \, x^{9} + 13860 \, x^{8} + 33264 \, x^{7} + 58212 \, x^{6} + 77616 \, x^{5} + 83160 \, x^{4} + 83160 \, x^{3} + 27720 \, x^{2} \log \left (x\right ) - 5544 \, x - 252}{504 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 1)^5*(x + 1)/x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.255058, size = 65, normalized size = 0.93 \[ \frac{x^{9}}{9} + \frac{11 x^{8}}{8} + \frac{55 x^{7}}{7} + \frac{55 x^{6}}{2} + 66 x^{5} + \frac{231 x^{4}}{2} + 154 x^{3} + 165 x^{2} + 165 x + 55 \log{\left (x \right )} - \frac{22 x + 1}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1+x)*(x**2+2*x+1)**5/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.270392, size = 80, normalized size = 1.14 \[ \frac{1}{9} \, x^{9} + \frac{11}{8} \, x^{8} + \frac{55}{7} \, x^{7} + \frac{55}{2} \, x^{6} + 66 \, x^{5} + \frac{231}{2} \, x^{4} + 154 \, x^{3} + 165 \, x^{2} + 165 \, x - \frac{22 \, x + 1}{2 \, x^{2}} + 55 \,{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 1)^5*(x + 1)/x^3,x, algorithm="giac")
[Out]