Optimal. Leaf size=19 \[ \frac{1}{13} (x+1)^{13}-\frac{1}{12} (x+1)^{12} \]
[Out]
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Rubi [A] time = 0.0174122, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{1}{13} (x+1)^{13}-\frac{1}{12} (x+1)^{12} \]
Antiderivative was successfully verified.
[In] Int[x*(1 + x)*(1 + 2*x + x^2)^5,x]
[Out]
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Rubi in Sympy [A] time = 8.58325, size = 12, normalized size = 0.63 \[ \frac{\left (x + 1\right )^{13}}{13} - \frac{\left (x + 1\right )^{12}}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(1+x)*(x**2+2*x+1)**5,x)
[Out]
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Mathematica [B] time = 0.00215253, size = 77, normalized size = 4.05 \[ \frac{x^{13}}{13}+\frac{11 x^{12}}{12}+5 x^{11}+\frac{33 x^{10}}{2}+\frac{110 x^9}{3}+\frac{231 x^8}{4}+66 x^7+55 x^6+33 x^5+\frac{55 x^4}{4}+\frac{11 x^3}{3}+\frac{x^2}{2} \]
Antiderivative was successfully verified.
[In] Integrate[x*(1 + x)*(1 + 2*x + x^2)^5,x]
[Out]
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Maple [B] time = 0.003, size = 62, normalized size = 3.3 \[{\frac{{x}^{13}}{13}}+{\frac{11\,{x}^{12}}{12}}+5\,{x}^{11}+{\frac{33\,{x}^{10}}{2}}+{\frac{110\,{x}^{9}}{3}}+{\frac{231\,{x}^{8}}{4}}+66\,{x}^{7}+55\,{x}^{6}+33\,{x}^{5}+{\frac{55\,{x}^{4}}{4}}+{\frac{11\,{x}^{3}}{3}}+{\frac{{x}^{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(1+x)*(x^2+2*x+1)^5,x)
[Out]
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Maxima [A] time = 0.692203, size = 82, normalized size = 4.32 \[ \frac{1}{13} \, x^{13} + \frac{11}{12} \, x^{12} + 5 \, x^{11} + \frac{33}{2} \, x^{10} + \frac{110}{3} \, x^{9} + \frac{231}{4} \, x^{8} + 66 \, x^{7} + 55 \, x^{6} + 33 \, x^{5} + \frac{55}{4} \, x^{4} + \frac{11}{3} \, x^{3} + \frac{1}{2} \, x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 1)^5*(x + 1)*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.248081, size = 1, normalized size = 0.05 \[ \frac{1}{13} x^{13} + \frac{11}{12} x^{12} + 5 x^{11} + \frac{33}{2} x^{10} + \frac{110}{3} x^{9} + \frac{231}{4} x^{8} + 66 x^{7} + 55 x^{6} + 33 x^{5} + \frac{55}{4} x^{4} + \frac{11}{3} x^{3} + \frac{1}{2} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 1)^5*(x + 1)*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.098685, size = 70, normalized size = 3.68 \[ \frac{x^{13}}{13} + \frac{11 x^{12}}{12} + 5 x^{11} + \frac{33 x^{10}}{2} + \frac{110 x^{9}}{3} + \frac{231 x^{8}}{4} + 66 x^{7} + 55 x^{6} + 33 x^{5} + \frac{55 x^{4}}{4} + \frac{11 x^{3}}{3} + \frac{x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(1+x)*(x**2+2*x+1)**5,x)
[Out]
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GIAC/XCAS [A] time = 0.269432, size = 82, normalized size = 4.32 \[ \frac{1}{13} \, x^{13} + \frac{11}{12} \, x^{12} + 5 \, x^{11} + \frac{33}{2} \, x^{10} + \frac{110}{3} \, x^{9} + \frac{231}{4} \, x^{8} + 66 \, x^{7} + 55 \, x^{6} + 33 \, x^{5} + \frac{55}{4} \, x^{4} + \frac{11}{3} \, x^{3} + \frac{1}{2} \, x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 1)^5*(x + 1)*x,x, algorithm="giac")
[Out]