Optimal. Leaf size=73 \[ -\frac{(x+1)^{12}}{17 x^{17}}+\frac{5 (x+1)^{12}}{272 x^{16}}-\frac{(x+1)^{12}}{204 x^{15}}+\frac{(x+1)^{12}}{952 x^{14}}-\frac{(x+1)^{12}}{6188 x^{13}}+\frac{(x+1)^{12}}{74256 x^{12}} \]
[Out]
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Rubi [A] time = 0.0507311, antiderivative size = 73, normalized size of antiderivative = 1., number of steps used = 7, number of rules used = 3, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.176 \[ -\frac{(x+1)^{12}}{17 x^{17}}+\frac{5 (x+1)^{12}}{272 x^{16}}-\frac{(x+1)^{12}}{204 x^{15}}+\frac{(x+1)^{12}}{952 x^{14}}-\frac{(x+1)^{12}}{6188 x^{13}}+\frac{(x+1)^{12}}{74256 x^{12}} \]
Antiderivative was successfully verified.
[In] Int[((1 + x)*(1 + 2*x + x^2)^5)/x^18,x]
[Out]
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Rubi in Sympy [A] time = 10.2645, size = 61, normalized size = 0.84 \[ \frac{\left (x + 1\right )^{12}}{74256 x^{12}} - \frac{\left (x + 1\right )^{12}}{6188 x^{13}} + \frac{\left (x + 1\right )^{12}}{952 x^{14}} - \frac{\left (x + 1\right )^{12}}{204 x^{15}} + \frac{5 \left (x + 1\right )^{12}}{272 x^{16}} - \frac{\left (x + 1\right )^{12}}{17 x^{17}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x)*(x**2+2*x+1)**5/x**18,x)
[Out]
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Mathematica [A] time = 0.00422186, size = 81, normalized size = 1.11 \[ -\frac{1}{17 x^{17}}-\frac{11}{16 x^{16}}-\frac{11}{3 x^{15}}-\frac{165}{14 x^{14}}-\frac{330}{13 x^{13}}-\frac{77}{2 x^{12}}-\frac{42}{x^{11}}-\frac{33}{x^{10}}-\frac{55}{3 x^9}-\frac{55}{8 x^8}-\frac{11}{7 x^7}-\frac{1}{6 x^6} \]
Antiderivative was successfully verified.
[In] Integrate[((1 + x)*(1 + 2*x + x^2)^5)/x^18,x]
[Out]
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Maple [A] time = 0.01, size = 62, normalized size = 0.9 \[ -{\frac{77}{2\,{x}^{12}}}-{\frac{11}{3\,{x}^{15}}}-{\frac{11}{16\,{x}^{16}}}-{\frac{330}{13\,{x}^{13}}}-{\frac{1}{6\,{x}^{6}}}-33\,{x}^{-10}-{\frac{1}{17\,{x}^{17}}}-{\frac{55}{8\,{x}^{8}}}-42\,{x}^{-11}-{\frac{165}{14\,{x}^{14}}}-{\frac{55}{3\,{x}^{9}}}-{\frac{11}{7\,{x}^{7}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x)*(x^2+2*x+1)^5/x^18,x)
[Out]
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Maxima [A] time = 0.691497, size = 81, normalized size = 1.11 \[ -\frac{12376 \, x^{11} + 116688 \, x^{10} + 510510 \, x^{9} + 1361360 \, x^{8} + 2450448 \, x^{7} + 3118752 \, x^{6} + 2858856 \, x^{5} + 1884960 \, x^{4} + 875160 \, x^{3} + 272272 \, x^{2} + 51051 \, x + 4368}{74256 \, x^{17}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 1)^5*(x + 1)/x^18,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.276059, size = 81, normalized size = 1.11 \[ -\frac{12376 \, x^{11} + 116688 \, x^{10} + 510510 \, x^{9} + 1361360 \, x^{8} + 2450448 \, x^{7} + 3118752 \, x^{6} + 2858856 \, x^{5} + 1884960 \, x^{4} + 875160 \, x^{3} + 272272 \, x^{2} + 51051 \, x + 4368}{74256 \, x^{17}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 1)^5*(x + 1)/x^18,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.659637, size = 61, normalized size = 0.84 \[ - \frac{12376 x^{11} + 116688 x^{10} + 510510 x^{9} + 1361360 x^{8} + 2450448 x^{7} + 3118752 x^{6} + 2858856 x^{5} + 1884960 x^{4} + 875160 x^{3} + 272272 x^{2} + 51051 x + 4368}{74256 x^{17}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1+x)*(x**2+2*x+1)**5/x**18,x)
[Out]
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GIAC/XCAS [A] time = 0.267583, size = 81, normalized size = 1.11 \[ -\frac{12376 \, x^{11} + 116688 \, x^{10} + 510510 \, x^{9} + 1361360 \, x^{8} + 2450448 \, x^{7} + 3118752 \, x^{6} + 2858856 \, x^{5} + 1884960 \, x^{4} + 875160 \, x^{3} + 272272 \, x^{2} + 51051 \, x + 4368}{74256 \, x^{17}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 1)^5*(x + 1)/x^18,x, algorithm="giac")
[Out]