Optimal. Leaf size=21 \[ \frac{4 x^5}{5}+\frac{4 x^3}{3}+2 x^2+x \]
[Out]
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Rubi [A] time = 0.00926799, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \frac{4 x^5}{5}+\frac{4 x^3}{3}+2 x^2+x \]
Antiderivative was successfully verified.
[In] Int[1 + 4*x + 4*x^2 + 4*x^4,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{4 x^{5}}{5} + \frac{4 x^{3}}{3} + x + 4 \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(4*x**4+4*x**2+4*x+1,x)
[Out]
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Mathematica [A] time = 0.000057277, size = 21, normalized size = 1. \[ \frac{4 x^5}{5}+\frac{4 x^3}{3}+2 x^2+x \]
Antiderivative was successfully verified.
[In] Integrate[1 + 4*x + 4*x^2 + 4*x^4,x]
[Out]
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Maple [A] time = 0.001, size = 18, normalized size = 0.9 \[ x+2\,{x}^{2}+{\frac{4\,{x}^{3}}{3}}+{\frac{4\,{x}^{5}}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(4*x^4+4*x^2+4*x+1,x)
[Out]
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Maxima [A] time = 0.808889, size = 23, normalized size = 1.1 \[ \frac{4}{5} \, x^{5} + \frac{4}{3} \, x^{3} + 2 \, x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(4*x^4 + 4*x^2 + 4*x + 1,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.237061, size = 1, normalized size = 0.05 \[ \frac{4}{5} x^{5} + \frac{4}{3} x^{3} + 2 x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(4*x^4 + 4*x^2 + 4*x + 1,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.059024, size = 19, normalized size = 0.9 \[ \frac{4 x^{5}}{5} + \frac{4 x^{3}}{3} + 2 x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(4*x**4+4*x**2+4*x+1,x)
[Out]
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GIAC/XCAS [A] time = 0.259678, size = 23, normalized size = 1.1 \[ \frac{4}{5} \, x^{5} + \frac{4}{3} \, x^{3} + 2 \, x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(4*x^4 + 4*x^2 + 4*x + 1,x, algorithm="giac")
[Out]