Optimal. Leaf size=75 \[ \frac{1}{5} a^3 A x^5+\frac{1}{6} a^2 x^6 (a B+3 A b)+\frac{1}{8} b^2 x^8 (3 a B+A b)+\frac{3}{7} a b x^7 (a B+A b)+\frac{1}{9} b^3 B x^9 \]
[Out]
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Rubi [A] time = 0.156713, antiderivative size = 75, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ \frac{1}{5} a^3 A x^5+\frac{1}{6} a^2 x^6 (a B+3 A b)+\frac{1}{8} b^2 x^8 (3 a B+A b)+\frac{3}{7} a b x^7 (a B+A b)+\frac{1}{9} b^3 B x^9 \]
Antiderivative was successfully verified.
[In] Int[x^4*(a + b*x)^3*(A + B*x),x]
[Out]
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Rubi in Sympy [A] time = 28.061, size = 70, normalized size = 0.93 \[ \frac{A a^{3} x^{5}}{5} + \frac{B b^{3} x^{9}}{9} + \frac{a^{2} x^{6} \left (3 A b + B a\right )}{6} + \frac{3 a b x^{7} \left (A b + B a\right )}{7} + \frac{b^{2} x^{8} \left (A b + 3 B a\right )}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**4*(b*x+a)**3*(B*x+A),x)
[Out]
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Mathematica [A] time = 0.0168775, size = 75, normalized size = 1. \[ \frac{1}{5} a^3 A x^5+\frac{1}{6} a^2 x^6 (a B+3 A b)+\frac{1}{8} b^2 x^8 (3 a B+A b)+\frac{3}{7} a b x^7 (a B+A b)+\frac{1}{9} b^3 B x^9 \]
Antiderivative was successfully verified.
[In] Integrate[x^4*(a + b*x)^3*(A + B*x),x]
[Out]
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Maple [A] time = 0.003, size = 76, normalized size = 1. \[{\frac{{b}^{3}B{x}^{9}}{9}}+{\frac{ \left ({b}^{3}A+3\,a{b}^{2}B \right ){x}^{8}}{8}}+{\frac{ \left ( 3\,a{b}^{2}A+3\,{a}^{2}bB \right ){x}^{7}}{7}}+{\frac{ \left ( 3\,{a}^{2}bA+{a}^{3}B \right ){x}^{6}}{6}}+{\frac{{a}^{3}A{x}^{5}}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^4*(b*x+a)^3*(B*x+A),x)
[Out]
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Maxima [A] time = 1.33958, size = 99, normalized size = 1.32 \[ \frac{1}{9} \, B b^{3} x^{9} + \frac{1}{5} \, A a^{3} x^{5} + \frac{1}{8} \,{\left (3 \, B a b^{2} + A b^{3}\right )} x^{8} + \frac{3}{7} \,{\left (B a^{2} b + A a b^{2}\right )} x^{7} + \frac{1}{6} \,{\left (B a^{3} + 3 \, A a^{2} b\right )} x^{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^3*x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.182428, size = 1, normalized size = 0.01 \[ \frac{1}{9} x^{9} b^{3} B + \frac{3}{8} x^{8} b^{2} a B + \frac{1}{8} x^{8} b^{3} A + \frac{3}{7} x^{7} b a^{2} B + \frac{3}{7} x^{7} b^{2} a A + \frac{1}{6} x^{6} a^{3} B + \frac{1}{2} x^{6} b a^{2} A + \frac{1}{5} x^{5} a^{3} A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^3*x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.140319, size = 82, normalized size = 1.09 \[ \frac{A a^{3} x^{5}}{5} + \frac{B b^{3} x^{9}}{9} + x^{8} \left (\frac{A b^{3}}{8} + \frac{3 B a b^{2}}{8}\right ) + x^{7} \left (\frac{3 A a b^{2}}{7} + \frac{3 B a^{2} b}{7}\right ) + x^{6} \left (\frac{A a^{2} b}{2} + \frac{B a^{3}}{6}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**4*(b*x+a)**3*(B*x+A),x)
[Out]
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GIAC/XCAS [A] time = 0.29354, size = 104, normalized size = 1.39 \[ \frac{1}{9} \, B b^{3} x^{9} + \frac{3}{8} \, B a b^{2} x^{8} + \frac{1}{8} \, A b^{3} x^{8} + \frac{3}{7} \, B a^{2} b x^{7} + \frac{3}{7} \, A a b^{2} x^{7} + \frac{1}{6} \, B a^{3} x^{6} + \frac{1}{2} \, A a^{2} b x^{6} + \frac{1}{5} \, A a^{3} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^3*x^4,x, algorithm="giac")
[Out]