Optimal. Leaf size=30 \[ \frac{8 x^5}{5}-\frac{15 x^4}{4}+\frac{8 x^3}{3}+12 x^2+8 x \]
[Out]
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Rubi [A] time = 0.0121648, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \frac{8 x^5}{5}-\frac{15 x^4}{4}+\frac{8 x^3}{3}+12 x^2+8 x \]
Antiderivative was successfully verified.
[In] Int[8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{8 x^{5}}{5} - \frac{15 x^{4}}{4} + \frac{8 x^{3}}{3} + 8 x + 24 \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(8*x**4-15*x**3+8*x**2+24*x+8,x)
[Out]
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Mathematica [A] time = 0.0000659165, size = 30, normalized size = 1. \[ \frac{8 x^5}{5}-\frac{15 x^4}{4}+\frac{8 x^3}{3}+12 x^2+8 x \]
Antiderivative was successfully verified.
[In] Integrate[8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4,x]
[Out]
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Maple [A] time = 0., size = 25, normalized size = 0.8 \[ 8\,x+12\,{x}^{2}+{\frac{8\,{x}^{3}}{3}}-{\frac{15\,{x}^{4}}{4}}+{\frac{8\,{x}^{5}}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(8*x^4-15*x^3+8*x^2+24*x+8,x)
[Out]
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Maxima [A] time = 0.800406, size = 32, normalized size = 1.07 \[ \frac{8}{5} \, x^{5} - \frac{15}{4} \, x^{4} + \frac{8}{3} \, x^{3} + 12 \, x^{2} + 8 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(8*x^4 - 15*x^3 + 8*x^2 + 24*x + 8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.232534, size = 1, normalized size = 0.03 \[ \frac{8}{5} x^{5} - \frac{15}{4} x^{4} + \frac{8}{3} x^{3} + 12 x^{2} + 8 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(8*x^4 - 15*x^3 + 8*x^2 + 24*x + 8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.062927, size = 27, normalized size = 0.9 \[ \frac{8 x^{5}}{5} - \frac{15 x^{4}}{4} + \frac{8 x^{3}}{3} + 12 x^{2} + 8 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(8*x**4-15*x**3+8*x**2+24*x+8,x)
[Out]
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GIAC/XCAS [A] time = 0.261141, size = 32, normalized size = 1.07 \[ \frac{8}{5} \, x^{5} - \frac{15}{4} \, x^{4} + \frac{8}{3} \, x^{3} + 12 \, x^{2} + 8 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(8*x^4 - 15*x^3 + 8*x^2 + 24*x + 8,x, algorithm="giac")
[Out]