Optimal. Leaf size=117 \[ \frac{1}{5} a^5 A x^5+\frac{1}{8} a^4 x^8 (a B+5 A b)+\frac{5}{11} a^3 b x^{11} (a B+2 A b)+\frac{5}{7} a^2 b^2 x^{14} (a B+A b)+\frac{1}{20} b^4 x^{20} (5 a B+A b)+\frac{5}{17} a b^3 x^{17} (2 a B+A b)+\frac{1}{23} b^5 B x^{23} \]
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Rubi [A] time = 0.249455, antiderivative size = 117, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{1}{5} a^5 A x^5+\frac{1}{8} a^4 x^8 (a B+5 A b)+\frac{5}{11} a^3 b x^{11} (a B+2 A b)+\frac{5}{7} a^2 b^2 x^{14} (a B+A b)+\frac{1}{20} b^4 x^{20} (5 a B+A b)+\frac{5}{17} a b^3 x^{17} (2 a B+A b)+\frac{1}{23} b^5 B x^{23} \]
Antiderivative was successfully verified.
[In] Int[x^4*(a + b*x^3)^5*(A + B*x^3),x]
[Out]
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Rubi in Sympy [A] time = 25.3733, size = 114, normalized size = 0.97 \[ \frac{A a^{5} x^{5}}{5} + \frac{B b^{5} x^{23}}{23} + \frac{a^{4} x^{8} \left (5 A b + B a\right )}{8} + \frac{5 a^{3} b x^{11} \left (2 A b + B a\right )}{11} + \frac{5 a^{2} b^{2} x^{14} \left (A b + B a\right )}{7} + \frac{5 a b^{3} x^{17} \left (A b + 2 B a\right )}{17} + \frac{b^{4} x^{20} \left (A b + 5 B a\right )}{20} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**4*(b*x**3+a)**5*(B*x**3+A),x)
[Out]
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Mathematica [A] time = 0.0326379, size = 117, normalized size = 1. \[ \frac{1}{5} a^5 A x^5+\frac{1}{8} a^4 x^8 (a B+5 A b)+\frac{5}{11} a^3 b x^{11} (a B+2 A b)+\frac{5}{7} a^2 b^2 x^{14} (a B+A b)+\frac{1}{20} b^4 x^{20} (5 a B+A b)+\frac{5}{17} a b^3 x^{17} (2 a B+A b)+\frac{1}{23} b^5 B x^{23} \]
Antiderivative was successfully verified.
[In] Integrate[x^4*(a + b*x^3)^5*(A + B*x^3),x]
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Maple [A] time = 0.003, size = 124, normalized size = 1.1 \[{\frac{{b}^{5}B{x}^{23}}{23}}+{\frac{ \left ({b}^{5}A+5\,a{b}^{4}B \right ){x}^{20}}{20}}+{\frac{ \left ( 5\,a{b}^{4}A+10\,{a}^{2}{b}^{3}B \right ){x}^{17}}{17}}+{\frac{ \left ( 10\,{a}^{2}{b}^{3}A+10\,{a}^{3}{b}^{2}B \right ){x}^{14}}{14}}+{\frac{ \left ( 10\,{a}^{3}{b}^{2}A+5\,{a}^{4}bB \right ){x}^{11}}{11}}+{\frac{ \left ( 5\,{a}^{4}bA+{a}^{5}B \right ){x}^{8}}{8}}+{\frac{{a}^{5}A{x}^{5}}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^4*(b*x^3+a)^5*(B*x^3+A),x)
[Out]
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Maxima [A] time = 1.45509, size = 161, normalized size = 1.38 \[ \frac{1}{23} \, B b^{5} x^{23} + \frac{1}{20} \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{20} + \frac{5}{17} \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{17} + \frac{5}{7} \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{14} + \frac{5}{11} \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{11} + \frac{1}{5} \, A a^{5} x^{5} + \frac{1}{8} \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^5*x^4,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.202253, size = 1, normalized size = 0.01 \[ \frac{1}{23} x^{23} b^{5} B + \frac{1}{4} x^{20} b^{4} a B + \frac{1}{20} x^{20} b^{5} A + \frac{10}{17} x^{17} b^{3} a^{2} B + \frac{5}{17} x^{17} b^{4} a A + \frac{5}{7} x^{14} b^{2} a^{3} B + \frac{5}{7} x^{14} b^{3} a^{2} A + \frac{5}{11} x^{11} b a^{4} B + \frac{10}{11} x^{11} b^{2} a^{3} A + \frac{1}{8} x^{8} a^{5} B + \frac{5}{8} x^{8} b a^{4} A + \frac{1}{5} x^{5} a^{5} A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^5*x^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.168105, size = 136, normalized size = 1.16 \[ \frac{A a^{5} x^{5}}{5} + \frac{B b^{5} x^{23}}{23} + x^{20} \left (\frac{A b^{5}}{20} + \frac{B a b^{4}}{4}\right ) + x^{17} \left (\frac{5 A a b^{4}}{17} + \frac{10 B a^{2} b^{3}}{17}\right ) + x^{14} \left (\frac{5 A a^{2} b^{3}}{7} + \frac{5 B a^{3} b^{2}}{7}\right ) + x^{11} \left (\frac{10 A a^{3} b^{2}}{11} + \frac{5 B a^{4} b}{11}\right ) + x^{8} \left (\frac{5 A a^{4} b}{8} + \frac{B a^{5}}{8}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**4*(b*x**3+a)**5*(B*x**3+A),x)
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GIAC/XCAS [A] time = 0.21534, size = 169, normalized size = 1.44 \[ \frac{1}{23} \, B b^{5} x^{23} + \frac{1}{4} \, B a b^{4} x^{20} + \frac{1}{20} \, A b^{5} x^{20} + \frac{10}{17} \, B a^{2} b^{3} x^{17} + \frac{5}{17} \, A a b^{4} x^{17} + \frac{5}{7} \, B a^{3} b^{2} x^{14} + \frac{5}{7} \, A a^{2} b^{3} x^{14} + \frac{5}{11} \, B a^{4} b x^{11} + \frac{10}{11} \, A a^{3} b^{2} x^{11} + \frac{1}{8} \, B a^{5} x^{8} + \frac{5}{8} \, A a^{4} b x^{8} + \frac{1}{5} \, A a^{5} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^5*x^4,x, algorithm="giac")
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