Optimal. Leaf size=109 \[ \frac{1}{4} a^2 A x^4+\frac{1}{5} a^2 B x^5+\frac{1}{8} b x^8 (2 a C+A b)+\frac{1}{6} a x^6 (a C+2 A b)+\frac{1}{9} b x^9 (2 a D+b B)+\frac{1}{7} a x^7 (a D+2 b B)+\frac{1}{10} b^2 C x^{10}+\frac{1}{11} b^2 D x^{11} \]
[Out]
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Rubi [A] time = 0.258931, antiderivative size = 109, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 28, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.036 \[ \frac{1}{4} a^2 A x^4+\frac{1}{5} a^2 B x^5+\frac{1}{8} b x^8 (2 a C+A b)+\frac{1}{6} a x^6 (a C+2 A b)+\frac{1}{9} b x^9 (2 a D+b B)+\frac{1}{7} a x^7 (a D+2 b B)+\frac{1}{10} b^2 C x^{10}+\frac{1}{11} b^2 D x^{11} \]
Antiderivative was successfully verified.
[In] Int[x^3*(a + b*x^2)^2*(A + B*x + C*x^2 + D*x^3),x]
[Out]
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Rubi in Sympy [A] time = 35.6268, size = 100, normalized size = 0.92 \[ \frac{A a^{2} x^{4}}{4} + \frac{B a^{2} x^{5}}{5} + \frac{C b^{2} x^{10}}{10} + \frac{D b^{2} x^{11}}{11} + \frac{a x^{7} \left (2 B b + D a\right )}{7} + \frac{a x^{6} \left (2 A b + C a\right )}{6} + \frac{b x^{9} \left (B b + 2 D a\right )}{9} + \frac{b x^{8} \left (A b + 2 C a\right )}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3*(b*x**2+a)**2*(D*x**3+C*x**2+B*x+A),x)
[Out]
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Mathematica [A] time = 0.0853129, size = 98, normalized size = 0.9 \[ a^2 \left (\frac{A x^4}{4}+\frac{B x^5}{5}+\frac{1}{42} x^6 (7 C+6 D x)\right )+\frac{1}{252} a b x^6 (84 A+x (72 B+7 x (9 C+8 D x)))+\frac{b^2 x^8 \left (495 A+4 x \left (110 B+99 C x+90 D x^2\right )\right )}{3960} \]
Antiderivative was successfully verified.
[In] Integrate[x^3*(a + b*x^2)^2*(A + B*x + C*x^2 + D*x^3),x]
[Out]
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Maple [A] time = 0.003, size = 102, normalized size = 0.9 \[{\frac{{b}^{2}D{x}^{11}}{11}}+{\frac{{b}^{2}C{x}^{10}}{10}}+{\frac{ \left ({b}^{2}B+2\,abD \right ){x}^{9}}{9}}+{\frac{ \left ({b}^{2}A+2\,abC \right ){x}^{8}}{8}}+{\frac{ \left ( 2\,abB+{a}^{2}D \right ){x}^{7}}{7}}+{\frac{ \left ( 2\,abA+{a}^{2}C \right ){x}^{6}}{6}}+{\frac{{a}^{2}B{x}^{5}}{5}}+{\frac{{a}^{2}A{x}^{4}}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3*(b*x^2+a)^2*(D*x^3+C*x^2+B*x+A),x)
[Out]
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Maxima [A] time = 1.34693, size = 136, normalized size = 1.25 \[ \frac{1}{11} \, D b^{2} x^{11} + \frac{1}{10} \, C b^{2} x^{10} + \frac{1}{9} \,{\left (2 \, D a b + B b^{2}\right )} x^{9} + \frac{1}{8} \,{\left (2 \, C a b + A b^{2}\right )} x^{8} + \frac{1}{5} \, B a^{2} x^{5} + \frac{1}{7} \,{\left (D a^{2} + 2 \, B a b\right )} x^{7} + \frac{1}{4} \, A a^{2} x^{4} + \frac{1}{6} \,{\left (C a^{2} + 2 \, A a b\right )} x^{6} \]
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)^2*x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.205721, size = 1, normalized size = 0.01 \[ \frac{1}{11} x^{11} b^{2} D + \frac{1}{10} x^{10} b^{2} C + \frac{2}{9} x^{9} b a D + \frac{1}{9} x^{9} b^{2} B + \frac{1}{4} x^{8} b a C + \frac{1}{8} x^{8} b^{2} A + \frac{1}{7} x^{7} a^{2} D + \frac{2}{7} x^{7} b a B + \frac{1}{6} x^{6} a^{2} C + \frac{1}{3} x^{6} b a A + \frac{1}{5} x^{5} a^{2} B + \frac{1}{4} x^{4} a^{2} A \]
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)^2*x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.073911, size = 110, normalized size = 1.01 \[ \frac{A a^{2} x^{4}}{4} + \frac{B a^{2} x^{5}}{5} + \frac{C b^{2} x^{10}}{10} + \frac{D b^{2} x^{11}}{11} + x^{9} \left (\frac{B b^{2}}{9} + \frac{2 D a b}{9}\right ) + x^{8} \left (\frac{A b^{2}}{8} + \frac{C a b}{4}\right ) + x^{7} \left (\frac{2 B a b}{7} + \frac{D a^{2}}{7}\right ) + x^{6} \left (\frac{A a b}{3} + \frac{C a^{2}}{6}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3*(b*x**2+a)**2*(D*x**3+C*x**2+B*x+A),x)
[Out]
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GIAC/XCAS [A] time = 0.208021, size = 142, normalized size = 1.3 \[ \frac{1}{11} \, D b^{2} x^{11} + \frac{1}{10} \, C b^{2} x^{10} + \frac{2}{9} \, D a b x^{9} + \frac{1}{9} \, B b^{2} x^{9} + \frac{1}{4} \, C a b x^{8} + \frac{1}{8} \, A b^{2} x^{8} + \frac{1}{7} \, D a^{2} x^{7} + \frac{2}{7} \, B a b x^{7} + \frac{1}{6} \, C a^{2} x^{6} + \frac{1}{3} \, A a b x^{6} + \frac{1}{5} \, B a^{2} x^{5} + \frac{1}{4} \, A a^{2} x^{4} \]
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)^2*x^3,x, algorithm="giac")
[Out]