Optimal. Leaf size=72 \[ a^2 x+\frac{2}{5} (64-a) x^5-2 (16-a) x^4+\frac{16}{3} (4-a) x^3+8 a x^2+\frac{x^9}{9}-x^8+\frac{32 x^7}{7}-\frac{40 x^6}{3} \]
[Out]
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Rubi [A] time = 0.0600135, antiderivative size = 72, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ a^2 x+\frac{2}{5} (64-a) x^5-2 (16-a) x^4+\frac{16}{3} (4-a) x^3+8 a x^2+\frac{x^9}{9}-x^8+\frac{32 x^7}{7}-\frac{40 x^6}{3} \]
Antiderivative was successfully verified.
[In] Int[(a + 8*x - 8*x^2 + 4*x^3 - x^4)^2,x]
[Out]
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Rubi in Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-x**4+4*x**3-8*x**2+a+8*x)**2,x)
[Out]
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Mathematica [A] time = 0.0140277, size = 66, normalized size = 0.92 \[ a^2 x-\frac{2}{5} (a-64) x^5+2 (a-16) x^4-\frac{16}{3} (a-4) x^3+8 a x^2+\frac{x^9}{9}-x^8+\frac{32 x^7}{7}-\frac{40 x^6}{3} \]
Antiderivative was successfully verified.
[In] Integrate[(a + 8*x - 8*x^2 + 4*x^3 - x^4)^2,x]
[Out]
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Maple [A] time = 0.001, size = 63, normalized size = 0.9 \[{\frac{{x}^{9}}{9}}-{x}^{8}+{\frac{32\,{x}^{7}}{7}}-{\frac{40\,{x}^{6}}{3}}+{\frac{ \left ( -2\,a+128 \right ){x}^{5}}{5}}+{\frac{ \left ( 8\,a-128 \right ){x}^{4}}{4}}+{\frac{ \left ( -16\,a+64 \right ){x}^{3}}{3}}+8\,a{x}^{2}+{a}^{2}x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-x^4+4*x^3-8*x^2+a+8*x)^2,x)
[Out]
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Maxima [A] time = 0.802978, size = 88, normalized size = 1.22 \[ \frac{1}{9} \, x^{9} - x^{8} + \frac{32}{7} \, x^{7} - \frac{40}{3} \, x^{6} + \frac{128}{5} \, x^{5} - 32 \, x^{4} + a^{2} x + \frac{64}{3} \, x^{3} - \frac{2}{15} \,{\left (3 \, x^{5} - 15 \, x^{4} + 40 \, x^{3} - 60 \, x^{2}\right )} a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^4 - 4*x^3 + 8*x^2 - a - 8*x)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.259592, size = 1, normalized size = 0.01 \[ \frac{1}{9} x^{9} - x^{8} + \frac{32}{7} x^{7} - \frac{40}{3} x^{6} - \frac{2}{5} x^{5} a + \frac{128}{5} x^{5} + 2 x^{4} a - 32 x^{4} - \frac{16}{3} x^{3} a + \frac{64}{3} x^{3} + 8 x^{2} a + x a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^4 - 4*x^3 + 8*x^2 - a - 8*x)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.106636, size = 65, normalized size = 0.9 \[ a^{2} x + 8 a x^{2} + \frac{x^{9}}{9} - x^{8} + \frac{32 x^{7}}{7} - \frac{40 x^{6}}{3} + x^{5} \left (- \frac{2 a}{5} + \frac{128}{5}\right ) + x^{4} \left (2 a - 32\right ) + x^{3} \left (- \frac{16 a}{3} + \frac{64}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-x**4+4*x**3-8*x**2+a+8*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.262786, size = 88, normalized size = 1.22 \[ \frac{1}{9} \, x^{9} - x^{8} + \frac{32}{7} \, x^{7} - \frac{2}{5} \, a x^{5} - \frac{40}{3} \, x^{6} + 2 \, a x^{4} + \frac{128}{5} \, x^{5} - \frac{16}{3} \, a x^{3} - 32 \, x^{4} + a^{2} x + 8 \, a x^{2} + \frac{64}{3} \, x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^4 - 4*x^3 + 8*x^2 - a - 8*x)^2,x, algorithm="giac")
[Out]