Optimal. Leaf size=95 \[ \frac{a^2 \left (a+b x^3\right )^6 (A b-a B)}{18 b^4}+\frac{\left (a+b x^3\right )^8 (A b-3 a B)}{24 b^4}-\frac{a \left (a+b x^3\right )^7 (2 A b-3 a B)}{21 b^4}+\frac{B \left (a+b x^3\right )^9}{27 b^4} \]
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Rubi [A] time = 0.607123, antiderivative size = 95, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ \frac{a^2 \left (a+b x^3\right )^6 (A b-a B)}{18 b^4}+\frac{\left (a+b x^3\right )^8 (A b-3 a B)}{24 b^4}-\frac{a \left (a+b x^3\right )^7 (2 A b-3 a B)}{21 b^4}+\frac{B \left (a+b x^3\right )^9}{27 b^4} \]
Antiderivative was successfully verified.
[In] Int[x^8*(a + b*x^3)^5*(A + B*x^3),x]
[Out]
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Rubi in Sympy [A] time = 30.6162, size = 85, normalized size = 0.89 \[ \frac{B \left (a + b x^{3}\right )^{9}}{27 b^{4}} + \frac{a^{2} \left (a + b x^{3}\right )^{6} \left (A b - B a\right )}{18 b^{4}} - \frac{a \left (a + b x^{3}\right )^{7} \left (2 A b - 3 B a\right )}{21 b^{4}} + \frac{\left (a + b x^{3}\right )^{8} \left (A b - 3 B a\right )}{24 b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**8*(b*x**3+a)**5*(B*x**3+A),x)
[Out]
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Mathematica [A] time = 0.0551935, size = 107, normalized size = 1.13 \[ \frac{x^9 \left (168 a^5 A+126 a^4 x^3 (a B+5 A b)+504 a^3 b x^6 (a B+2 A b)+840 a^2 b^2 x^9 (a B+A b)+63 b^4 x^{15} (5 a B+A b)+360 a b^3 x^{12} (2 a B+A b)+56 b^5 B x^{18}\right )}{1512} \]
Antiderivative was successfully verified.
[In] Integrate[x^8*(a + b*x^3)^5*(A + B*x^3),x]
[Out]
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Maple [A] time = 0.002, size = 124, normalized size = 1.3 \[{\frac{{b}^{5}B{x}^{27}}{27}}+{\frac{ \left ({b}^{5}A+5\,a{b}^{4}B \right ){x}^{24}}{24}}+{\frac{ \left ( 5\,a{b}^{4}A+10\,{a}^{2}{b}^{3}B \right ){x}^{21}}{21}}+{\frac{ \left ( 10\,{a}^{2}{b}^{3}A+10\,{a}^{3}{b}^{2}B \right ){x}^{18}}{18}}+{\frac{ \left ( 10\,{a}^{3}{b}^{2}A+5\,{a}^{4}bB \right ){x}^{15}}{15}}+{\frac{ \left ( 5\,{a}^{4}bA+{a}^{5}B \right ){x}^{12}}{12}}+{\frac{{a}^{5}A{x}^{9}}{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^8*(b*x^3+a)^5*(B*x^3+A),x)
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Maxima [A] time = 1.41794, size = 161, normalized size = 1.69 \[ \frac{1}{27} \, B b^{5} x^{27} + \frac{1}{24} \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{24} + \frac{5}{21} \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{21} + \frac{5}{9} \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{18} + \frac{1}{3} \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{15} + \frac{1}{9} \, A a^{5} x^{9} + \frac{1}{12} \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^5*x^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.193193, size = 1, normalized size = 0.01 \[ \frac{1}{27} x^{27} b^{5} B + \frac{5}{24} x^{24} b^{4} a B + \frac{1}{24} x^{24} b^{5} A + \frac{10}{21} x^{21} b^{3} a^{2} B + \frac{5}{21} x^{21} b^{4} a A + \frac{5}{9} x^{18} b^{2} a^{3} B + \frac{5}{9} x^{18} b^{3} a^{2} A + \frac{1}{3} x^{15} b a^{4} B + \frac{2}{3} x^{15} b^{2} a^{3} A + \frac{1}{12} x^{12} a^{5} B + \frac{5}{12} x^{12} b a^{4} A + \frac{1}{9} x^{9} a^{5} A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^5*x^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.168798, size = 136, normalized size = 1.43 \[ \frac{A a^{5} x^{9}}{9} + \frac{B b^{5} x^{27}}{27} + x^{24} \left (\frac{A b^{5}}{24} + \frac{5 B a b^{4}}{24}\right ) + x^{21} \left (\frac{5 A a b^{4}}{21} + \frac{10 B a^{2} b^{3}}{21}\right ) + x^{18} \left (\frac{5 A a^{2} b^{3}}{9} + \frac{5 B a^{3} b^{2}}{9}\right ) + x^{15} \left (\frac{2 A a^{3} b^{2}}{3} + \frac{B a^{4} b}{3}\right ) + x^{12} \left (\frac{5 A a^{4} b}{12} + \frac{B a^{5}}{12}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**8*(b*x**3+a)**5*(B*x**3+A),x)
[Out]
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GIAC/XCAS [A] time = 0.215987, size = 169, normalized size = 1.78 \[ \frac{1}{27} \, B b^{5} x^{27} + \frac{5}{24} \, B a b^{4} x^{24} + \frac{1}{24} \, A b^{5} x^{24} + \frac{10}{21} \, B a^{2} b^{3} x^{21} + \frac{5}{21} \, A a b^{4} x^{21} + \frac{5}{9} \, B a^{3} b^{2} x^{18} + \frac{5}{9} \, A a^{2} b^{3} x^{18} + \frac{1}{3} \, B a^{4} b x^{15} + \frac{2}{3} \, A a^{3} b^{2} x^{15} + \frac{1}{12} \, B a^{5} x^{12} + \frac{5}{12} \, A a^{4} b x^{12} + \frac{1}{9} \, A a^{5} x^{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^5*x^8,x, algorithm="giac")
[Out]