Optimal. Leaf size=46 \[ \frac{1}{16} (x+1)^{16}-\frac{4}{15} (x+1)^{15}+\frac{3}{7} (x+1)^{14}-\frac{4}{13} (x+1)^{13}+\frac{1}{12} (x+1)^{12} \]
[Out]
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Rubi [A] time = 0.0446687, antiderivative size = 46, 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 \[ \frac{1}{16} (x+1)^{16}-\frac{4}{15} (x+1)^{15}+\frac{3}{7} (x+1)^{14}-\frac{4}{13} (x+1)^{13}+\frac{1}{12} (x+1)^{12} \]
Antiderivative was successfully verified.
[In] Int[x^4*(1 + x)*(1 + 2*x + x^2)^5,x]
[Out]
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Rubi in Sympy [A] time = 11.3113, size = 37, normalized size = 0.8 \[ \frac{\left (x + 1\right )^{16}}{16} - \frac{4 \left (x + 1\right )^{15}}{15} + \frac{3 \left (x + 1\right )^{14}}{7} - \frac{4 \left (x + 1\right )^{13}}{13} + \frac{\left (x + 1\right )^{12}}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**4*(1+x)*(x**2+2*x+1)**5,x)
[Out]
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Mathematica [A] time = 0.00246579, size = 83, normalized size = 1.8 \[ \frac{x^{16}}{16}+\frac{11 x^{15}}{15}+\frac{55 x^{14}}{14}+\frac{165 x^{13}}{13}+\frac{55 x^{12}}{2}+42 x^{11}+\frac{231 x^{10}}{5}+\frac{110 x^9}{3}+\frac{165 x^8}{8}+\frac{55 x^7}{7}+\frac{11 x^6}{6}+\frac{x^5}{5} \]
Antiderivative was successfully verified.
[In] Integrate[x^4*(1 + x)*(1 + 2*x + x^2)^5,x]
[Out]
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Maple [A] time = 0.002, size = 62, normalized size = 1.4 \[{\frac{{x}^{16}}{16}}+{\frac{11\,{x}^{15}}{15}}+{\frac{55\,{x}^{14}}{14}}+{\frac{165\,{x}^{13}}{13}}+{\frac{55\,{x}^{12}}{2}}+42\,{x}^{11}+{\frac{231\,{x}^{10}}{5}}+{\frac{110\,{x}^{9}}{3}}+{\frac{165\,{x}^{8}}{8}}+{\frac{55\,{x}^{7}}{7}}+{\frac{11\,{x}^{6}}{6}}+{\frac{{x}^{5}}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^4*(1+x)*(x^2+2*x+1)^5,x)
[Out]
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Maxima [A] time = 0.682295, size = 82, normalized size = 1.78 \[ \frac{1}{16} \, x^{16} + \frac{11}{15} \, x^{15} + \frac{55}{14} \, x^{14} + \frac{165}{13} \, x^{13} + \frac{55}{2} \, x^{12} + 42 \, x^{11} + \frac{231}{5} \, x^{10} + \frac{110}{3} \, x^{9} + \frac{165}{8} \, x^{8} + \frac{55}{7} \, x^{7} + \frac{11}{6} \, x^{6} + \frac{1}{5} \, x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 1)^5*(x + 1)*x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.25929, size = 1, normalized size = 0.02 \[ \frac{1}{16} x^{16} + \frac{11}{15} x^{15} + \frac{55}{14} x^{14} + \frac{165}{13} x^{13} + \frac{55}{2} x^{12} + 42 x^{11} + \frac{231}{5} x^{10} + \frac{110}{3} x^{9} + \frac{165}{8} x^{8} + \frac{55}{7} x^{7} + \frac{11}{6} x^{6} + \frac{1}{5} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 1)^5*(x + 1)*x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.104109, size = 75, normalized size = 1.63 \[ \frac{x^{16}}{16} + \frac{11 x^{15}}{15} + \frac{55 x^{14}}{14} + \frac{165 x^{13}}{13} + \frac{55 x^{12}}{2} + 42 x^{11} + \frac{231 x^{10}}{5} + \frac{110 x^{9}}{3} + \frac{165 x^{8}}{8} + \frac{55 x^{7}}{7} + \frac{11 x^{6}}{6} + \frac{x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**4*(1+x)*(x**2+2*x+1)**5,x)
[Out]
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GIAC/XCAS [A] time = 0.276003, size = 82, normalized size = 1.78 \[ \frac{1}{16} \, x^{16} + \frac{11}{15} \, x^{15} + \frac{55}{14} \, x^{14} + \frac{165}{13} \, x^{13} + \frac{55}{2} \, x^{12} + 42 \, x^{11} + \frac{231}{5} \, x^{10} + \frac{110}{3} \, x^{9} + \frac{165}{8} \, x^{8} + \frac{55}{7} \, x^{7} + \frac{11}{6} \, x^{6} + \frac{1}{5} \, x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 1)^5*(x + 1)*x^4,x, algorithm="giac")
[Out]