Optimal. Leaf size=65 \[ \frac{1}{5} x^5 (a C+A b)+\frac{1}{3} a A x^3+\frac{1}{6} x^6 (a D+b B)+\frac{1}{4} a B x^4+\frac{1}{7} b C x^7+\frac{1}{8} b D x^8 \]
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Rubi [A] time = 0.147951, antiderivative size = 65, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.038 \[ \frac{1}{5} x^5 (a C+A b)+\frac{1}{3} a A x^3+\frac{1}{6} x^6 (a D+b B)+\frac{1}{4} a B x^4+\frac{1}{7} b C x^7+\frac{1}{8} b D x^8 \]
Antiderivative was successfully verified.
[In] Int[x^2*(a + b*x^2)*(A + B*x + C*x^2 + D*x^3),x]
[Out]
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Rubi in Sympy [A] time = 25.7079, size = 60, normalized size = 0.92 \[ \frac{A a x^{3}}{3} + \frac{B a x^{4}}{4} + \frac{C b x^{7}}{7} + \frac{D b x^{8}}{8} + x^{6} \left (\frac{B b}{6} + \frac{D a}{6}\right ) + x^{5} \left (\frac{A b}{5} + \frac{C a}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*(b*x**2+a)*(D*x**3+C*x**2+B*x+A),x)
[Out]
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Mathematica [A] time = 0.0295779, size = 65, normalized size = 1. \[ \frac{1}{5} x^5 (a C+A b)+\frac{1}{3} a A x^3+\frac{1}{6} x^6 (a D+b B)+\frac{1}{4} a B x^4+\frac{1}{7} b C x^7+\frac{1}{8} b D x^8 \]
Antiderivative was successfully verified.
[In] Integrate[x^2*(a + b*x^2)*(A + B*x + C*x^2 + D*x^3),x]
[Out]
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Maple [A] time = 0.002, size = 54, normalized size = 0.8 \[{\frac{aA{x}^{3}}{3}}+{\frac{aB{x}^{4}}{4}}+{\frac{ \left ( Ab+aC \right ){x}^{5}}{5}}+{\frac{ \left ( Bb+aD \right ){x}^{6}}{6}}+{\frac{bC{x}^{7}}{7}}+{\frac{bD{x}^{8}}{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*(b*x^2+a)*(D*x^3+C*x^2+B*x+A),x)
[Out]
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Maxima [A] time = 1.34727, size = 72, normalized size = 1.11 \[ \frac{1}{8} \, D b x^{8} + \frac{1}{7} \, C b x^{7} + \frac{1}{6} \,{\left (D a + B b\right )} x^{6} + \frac{1}{4} \, B a x^{4} + \frac{1}{5} \,{\left (C a + A b\right )} x^{5} + \frac{1}{3} \, A a x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((D*x^3 + C*x^2 + B*x + A)*(b*x^2 + a)*x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.258405, size = 1, normalized size = 0.02 \[ \frac{1}{8} x^{8} b D + \frac{1}{7} x^{7} b C + \frac{1}{6} x^{6} a D + \frac{1}{6} x^{6} b B + \frac{1}{5} x^{5} a C + \frac{1}{5} x^{5} b A + \frac{1}{4} x^{4} a B + \frac{1}{3} x^{3} a A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((D*x^3 + C*x^2 + B*x + A)*(b*x^2 + a)*x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.053457, size = 60, normalized size = 0.92 \[ \frac{A a x^{3}}{3} + \frac{B a x^{4}}{4} + \frac{C b x^{7}}{7} + \frac{D b x^{8}}{8} + x^{6} \left (\frac{B b}{6} + \frac{D a}{6}\right ) + x^{5} \left (\frac{A b}{5} + \frac{C a}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2*(b*x**2+a)*(D*x**3+C*x**2+B*x+A),x)
[Out]
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GIAC/XCAS [A] time = 0.212686, size = 77, normalized size = 1.18 \[ \frac{1}{8} \, D b x^{8} + \frac{1}{7} \, C b x^{7} + \frac{1}{6} \, D a x^{6} + \frac{1}{6} \, B b x^{6} + \frac{1}{5} \, C a x^{5} + \frac{1}{5} \, A b x^{5} + \frac{1}{4} \, B a x^{4} + \frac{1}{3} \, A a x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((D*x^3 + C*x^2 + B*x + A)*(b*x^2 + a)*x^2,x, algorithm="giac")
[Out]