Optimal. Leaf size=45 \[ \frac{16 x^9}{9}+\frac{32 x^7}{7}+\frac{16 x^6}{3}+\frac{24 x^5}{5}+8 x^4+8 x^3+4 x^2+x \]
[Out]
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Rubi [A] time = 0.0297536, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{16 x^9}{9}+\frac{32 x^7}{7}+\frac{16 x^6}{3}+\frac{24 x^5}{5}+8 x^4+8 x^3+4 x^2+x \]
Antiderivative was successfully verified.
[In] Int[(1 + 4*x + 4*x^2 + 4*x^4)^2,x]
[Out]
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Rubi in Sympy [A] time = 24.129, size = 42, normalized size = 0.93 \[ \frac{16 x^{9}}{9} + \frac{32 x^{7}}{7} + \frac{16 x^{6}}{3} + \frac{24 x^{5}}{5} + 8 x^{4} + 8 x^{3} + 4 x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((4*x**4+4*x**2+4*x+1)**2,x)
[Out]
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Mathematica [A] time = 0.0018479, size = 45, normalized size = 1. \[ \frac{16 x^9}{9}+\frac{32 x^7}{7}+\frac{16 x^6}{3}+\frac{24 x^5}{5}+8 x^4+8 x^3+4 x^2+x \]
Antiderivative was successfully verified.
[In] Integrate[(1 + 4*x + 4*x^2 + 4*x^4)^2,x]
[Out]
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Maple [A] time = 0.001, size = 38, normalized size = 0.8 \[ x+4\,{x}^{2}+8\,{x}^{3}+8\,{x}^{4}+{\frac{24\,{x}^{5}}{5}}+{\frac{16\,{x}^{6}}{3}}+{\frac{32\,{x}^{7}}{7}}+{\frac{16\,{x}^{9}}{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((4*x^4+4*x^2+4*x+1)^2,x)
[Out]
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Maxima [A] time = 0.785279, size = 50, normalized size = 1.11 \[ \frac{16}{9} \, x^{9} + \frac{32}{7} \, x^{7} + \frac{16}{3} \, x^{6} + \frac{24}{5} \, x^{5} + 8 \, x^{4} + 8 \, x^{3} + 4 \, x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x^4 + 4*x^2 + 4*x + 1)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.222767, size = 1, normalized size = 0.02 \[ \frac{16}{9} x^{9} + \frac{32}{7} x^{7} + \frac{16}{3} x^{6} + \frac{24}{5} x^{5} + 8 x^{4} + 8 x^{3} + 4 x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x^4 + 4*x^2 + 4*x + 1)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.076658, size = 42, normalized size = 0.93 \[ \frac{16 x^{9}}{9} + \frac{32 x^{7}}{7} + \frac{16 x^{6}}{3} + \frac{24 x^{5}}{5} + 8 x^{4} + 8 x^{3} + 4 x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x**4+4*x**2+4*x+1)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.259937, size = 50, normalized size = 1.11 \[ \frac{16}{9} \, x^{9} + \frac{32}{7} \, x^{7} + \frac{16}{3} \, x^{6} + \frac{24}{5} \, x^{5} + 8 \, x^{4} + 8 \, x^{3} + 4 \, x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x^4 + 4*x^2 + 4*x + 1)^2,x, algorithm="giac")
[Out]