Optimal. Leaf size=113 \[ -\frac{a^5 A}{8 x^8}-\frac{a^4 (a B+5 A b)}{5 x^5}-\frac{5 a^3 b (a B+2 A b)}{2 x^2}+10 a^2 b^2 x (a B+A b)+\frac{1}{7} b^4 x^7 (5 a B+A b)+\frac{5}{4} a b^3 x^4 (2 a B+A b)+\frac{1}{10} b^5 B x^{10} \]
[Out]
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Rubi [A] time = 0.207752, antiderivative size = 113, 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 \[ -\frac{a^5 A}{8 x^8}-\frac{a^4 (a B+5 A b)}{5 x^5}-\frac{5 a^3 b (a B+2 A b)}{2 x^2}+10 a^2 b^2 x (a B+A b)+\frac{1}{7} b^4 x^7 (5 a B+A b)+\frac{5}{4} a b^3 x^4 (2 a B+A b)+\frac{1}{10} b^5 B x^{10} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^3)^5*(A + B*x^3))/x^9,x]
[Out]
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Rubi in Sympy [A] time = 25.7418, size = 110, normalized size = 0.97 \[ - \frac{A a^{5}}{8 x^{8}} + \frac{B b^{5} x^{10}}{10} - \frac{a^{4} \left (5 A b + B a\right )}{5 x^{5}} - \frac{5 a^{3} b \left (2 A b + B a\right )}{2 x^{2}} + 10 a^{2} b^{2} x \left (A b + B a\right ) + \frac{5 a b^{3} x^{4} \left (A b + 2 B a\right )}{4} + \frac{b^{4} x^{7} \left (A b + 5 B a\right )}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**5*(B*x**3+A)/x**9,x)
[Out]
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Mathematica [A] time = 0.0696126, size = 113, normalized size = 1. \[ -\frac{a^5 A}{8 x^8}-\frac{a^4 (a B+5 A b)}{5 x^5}-\frac{5 a^3 b (a B+2 A b)}{2 x^2}+10 a^2 b^2 x (a B+A b)+\frac{1}{7} b^4 x^7 (5 a B+A b)+\frac{5}{4} a b^3 x^4 (2 a B+A b)+\frac{1}{10} b^5 B x^{10} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^3)^5*(A + B*x^3))/x^9,x]
[Out]
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Maple [A] time = 0.01, size = 114, normalized size = 1. \[{\frac{{b}^{5}B{x}^{10}}{10}}+{\frac{A{x}^{7}{b}^{5}}{7}}+{\frac{5\,B{x}^{7}a{b}^{4}}{7}}+{\frac{5\,A{x}^{4}a{b}^{4}}{4}}+{\frac{5\,B{x}^{4}{a}^{2}{b}^{3}}{2}}+10\,Ax{a}^{2}{b}^{3}+10\,Bx{a}^{3}{b}^{2}-{\frac{A{a}^{5}}{8\,{x}^{8}}}-{\frac{5\,{a}^{3}b \left ( 2\,Ab+Ba \right ) }{2\,{x}^{2}}}-{\frac{{a}^{4} \left ( 5\,Ab+Ba \right ) }{5\,{x}^{5}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^5*(B*x^3+A)/x^9,x)
[Out]
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Maxima [A] time = 1.36257, size = 162, normalized size = 1.43 \[ \frac{1}{10} \, B b^{5} x^{10} + \frac{1}{7} \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{7} + \frac{5}{4} \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{4} + 10 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x - \frac{100 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} + 5 \, A a^{5} + 8 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{40 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^5/x^9,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.225617, size = 163, normalized size = 1.44 \[ \frac{28 \, B b^{5} x^{18} + 40 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 350 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} + 2800 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} - 700 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} - 35 \, A a^{5} - 56 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{280 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^5/x^9,x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.90022, size = 129, normalized size = 1.14 \[ \frac{B b^{5} x^{10}}{10} + x^{7} \left (\frac{A b^{5}}{7} + \frac{5 B a b^{4}}{7}\right ) + x^{4} \left (\frac{5 A a b^{4}}{4} + \frac{5 B a^{2} b^{3}}{2}\right ) + x \left (10 A a^{2} b^{3} + 10 B a^{3} b^{2}\right ) - \frac{5 A a^{5} + x^{6} \left (200 A a^{3} b^{2} + 100 B a^{4} b\right ) + x^{3} \left (40 A a^{4} b + 8 B a^{5}\right )}{40 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**5*(B*x**3+A)/x**9,x)
[Out]
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GIAC/XCAS [A] time = 0.217837, size = 167, normalized size = 1.48 \[ \frac{1}{10} \, B b^{5} x^{10} + \frac{5}{7} \, B a b^{4} x^{7} + \frac{1}{7} \, A b^{5} x^{7} + \frac{5}{2} \, B a^{2} b^{3} x^{4} + \frac{5}{4} \, A a b^{4} x^{4} + 10 \, B a^{3} b^{2} x + 10 \, A a^{2} b^{3} x - \frac{100 \, B a^{4} b x^{6} + 200 \, A a^{3} b^{2} x^{6} + 8 \, B a^{5} x^{3} + 40 \, A a^{4} b x^{3} + 5 \, A a^{5}}{40 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^5/x^9,x, algorithm="giac")
[Out]