Optimal. Leaf size=69 \[ \frac{64 x^{13}}{13}+\frac{192 x^{11}}{11}+\frac{96 x^{10}}{5}+\frac{80 x^9}{3}+48 x^8+\frac{352 x^7}{7}+48 x^6+\frac{252 x^5}{5}+40 x^4+20 x^3+6 x^2+x \]
[Out]
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Rubi [A] time = 0.0415652, antiderivative size = 69, 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 \[ \frac{64 x^{13}}{13}+\frac{192 x^{11}}{11}+\frac{96 x^{10}}{5}+\frac{80 x^9}{3}+48 x^8+\frac{352 x^7}{7}+48 x^6+\frac{252 x^5}{5}+40 x^4+20 x^3+6 x^2+x \]
Antiderivative was successfully verified.
[In] Int[(1 + 4*x + 4*x^2 + 4*x^4)^3,x]
[Out]
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Rubi in Sympy [A] time = 31.7697, size = 66, normalized size = 0.96 \[ \frac{64 x^{13}}{13} + \frac{192 x^{11}}{11} + \frac{96 x^{10}}{5} + \frac{80 x^{9}}{3} + 48 x^{8} + \frac{352 x^{7}}{7} + 48 x^{6} + \frac{252 x^{5}}{5} + 40 x^{4} + 20 x^{3} + 6 x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((4*x**4+4*x**2+4*x+1)**3,x)
[Out]
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Mathematica [A] time = 0.00142392, size = 69, normalized size = 1. \[ \frac{64 x^{13}}{13}+\frac{192 x^{11}}{11}+\frac{96 x^{10}}{5}+\frac{80 x^9}{3}+48 x^8+\frac{352 x^7}{7}+48 x^6+\frac{252 x^5}{5}+40 x^4+20 x^3+6 x^2+x \]
Antiderivative was successfully verified.
[In] Integrate[(1 + 4*x + 4*x^2 + 4*x^4)^3,x]
[Out]
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Maple [A] time = 0.002, size = 58, normalized size = 0.8 \[ x+6\,{x}^{2}+20\,{x}^{3}+40\,{x}^{4}+{\frac{252\,{x}^{5}}{5}}+48\,{x}^{6}+{\frac{352\,{x}^{7}}{7}}+48\,{x}^{8}+{\frac{80\,{x}^{9}}{3}}+{\frac{96\,{x}^{10}}{5}}+{\frac{192\,{x}^{11}}{11}}+{\frac{64\,{x}^{13}}{13}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((4*x^4+4*x^2+4*x+1)^3,x)
[Out]
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Maxima [A] time = 0.788934, size = 77, normalized size = 1.12 \[ \frac{64}{13} \, x^{13} + \frac{192}{11} \, x^{11} + \frac{96}{5} \, x^{10} + \frac{80}{3} \, x^{9} + 48 \, x^{8} + \frac{352}{7} \, x^{7} + 48 \, x^{6} + \frac{252}{5} \, x^{5} + 40 \, x^{4} + 20 \, x^{3} + 6 \, x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x^4 + 4*x^2 + 4*x + 1)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.227525, size = 1, normalized size = 0.01 \[ \frac{64}{13} x^{13} + \frac{192}{11} x^{11} + \frac{96}{5} x^{10} + \frac{80}{3} x^{9} + 48 x^{8} + \frac{352}{7} x^{7} + 48 x^{6} + \frac{252}{5} x^{5} + 40 x^{4} + 20 x^{3} + 6 x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x^4 + 4*x^2 + 4*x + 1)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.093272, size = 66, normalized size = 0.96 \[ \frac{64 x^{13}}{13} + \frac{192 x^{11}}{11} + \frac{96 x^{10}}{5} + \frac{80 x^{9}}{3} + 48 x^{8} + \frac{352 x^{7}}{7} + 48 x^{6} + \frac{252 x^{5}}{5} + 40 x^{4} + 20 x^{3} + 6 x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x**4+4*x**2+4*x+1)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.259721, size = 77, normalized size = 1.12 \[ \frac{64}{13} \, x^{13} + \frac{192}{11} \, x^{11} + \frac{96}{5} \, x^{10} + \frac{80}{3} \, x^{9} + 48 \, x^{8} + \frac{352}{7} \, x^{7} + 48 \, x^{6} + \frac{252}{5} \, x^{5} + 40 \, x^{4} + 20 \, x^{3} + 6 \, x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x^4 + 4*x^2 + 4*x + 1)^3,x, algorithm="giac")
[Out]