Optimal. Leaf size=114 \[ -\frac{a^5 A}{6 x^6}-\frac{a^4 (a B+5 A b)}{3 x^3}+5 a^3 b \log (x) (a B+2 A b)+\frac{10}{3} a^2 b^2 x^3 (a B+A b)+\frac{1}{9} b^4 x^9 (5 a B+A b)+\frac{5}{6} a b^3 x^6 (2 a B+A b)+\frac{1}{12} b^5 B x^{12} \]
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Rubi [A] time = 0.314711, antiderivative size = 114, 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 \[ -\frac{a^5 A}{6 x^6}-\frac{a^4 (a B+5 A b)}{3 x^3}+5 a^3 b \log (x) (a B+2 A b)+\frac{10}{3} a^2 b^2 x^3 (a B+A b)+\frac{1}{9} b^4 x^9 (5 a B+A b)+\frac{5}{6} a b^3 x^6 (2 a B+A b)+\frac{1}{12} b^5 B x^{12} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^3)^5*(A + B*x^3))/x^7,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{A a^{5}}{6 x^{6}} + \frac{B b^{5} x^{12}}{12} - \frac{a^{4} \left (5 A b + B a\right )}{3 x^{3}} + \frac{5 a^{3} b \left (2 A b + B a\right ) \log{\left (x^{3} \right )}}{3} + \frac{10 a^{2} b^{2} x^{3} \left (A b + B a\right )}{3} + \frac{5 a b^{3} \left (A b + 2 B a\right ) \int ^{x^{3}} x\, dx}{3} + \frac{b^{4} x^{9} \left (A b + 5 B a\right )}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**5*(B*x**3+A)/x**7,x)
[Out]
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Mathematica [A] time = 0.0983266, size = 106, normalized size = 0.93 \[ \frac{1}{36} \left (-\frac{6 a^5 A}{x^6}-\frac{12 a^4 (a B+5 A b)}{x^3}+180 a^3 b \log (x) (a B+2 A b)+120 a^2 b^2 x^3 (a B+A b)+4 b^4 x^9 (5 a B+A b)+30 a b^3 x^6 (2 a B+A b)+3 b^5 B x^{12}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^3)^5*(A + B*x^3))/x^7,x]
[Out]
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Maple [A] time = 0.01, size = 124, normalized size = 1.1 \[{\frac{{b}^{5}B{x}^{12}}{12}}+{\frac{A{x}^{9}{b}^{5}}{9}}+{\frac{5\,B{x}^{9}a{b}^{4}}{9}}+{\frac{5\,A{x}^{6}a{b}^{4}}{6}}+{\frac{5\,B{x}^{6}{a}^{2}{b}^{3}}{3}}+{\frac{10\,A{x}^{3}{a}^{2}{b}^{3}}{3}}+{\frac{10\,B{x}^{3}{a}^{3}{b}^{2}}{3}}+10\,A\ln \left ( x \right ){a}^{3}{b}^{2}+5\,B\ln \left ( x \right ){a}^{4}b-{\frac{A{a}^{5}}{6\,{x}^{6}}}-{\frac{5\,{a}^{4}bA}{3\,{x}^{3}}}-{\frac{{a}^{5}B}{3\,{x}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^5*(B*x^3+A)/x^7,x)
[Out]
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Maxima [A] time = 1.37918, size = 165, normalized size = 1.45 \[ \frac{1}{12} \, B b^{5} x^{12} + \frac{1}{9} \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{9} + \frac{5}{6} \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{6} + \frac{10}{3} \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{3} + \frac{5}{3} \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} \log \left (x^{3}\right ) - \frac{A a^{5} + 2 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{6 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^5/x^7,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.221172, size = 166, normalized size = 1.46 \[ \frac{3 \, B b^{5} x^{18} + 4 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 30 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} + 120 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} + 180 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} \log \left (x\right ) - 6 \, A a^{5} - 12 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{36 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^5/x^7,x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.16125, size = 129, normalized size = 1.13 \[ \frac{B b^{5} x^{12}}{12} + 5 a^{3} b \left (2 A b + B a\right ) \log{\left (x \right )} + x^{9} \left (\frac{A b^{5}}{9} + \frac{5 B a b^{4}}{9}\right ) + x^{6} \left (\frac{5 A a b^{4}}{6} + \frac{5 B a^{2} b^{3}}{3}\right ) + x^{3} \left (\frac{10 A a^{2} b^{3}}{3} + \frac{10 B a^{3} b^{2}}{3}\right ) - \frac{A a^{5} + x^{3} \left (10 A a^{4} b + 2 B a^{5}\right )}{6 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**5*(B*x**3+A)/x**7,x)
[Out]
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GIAC/XCAS [A] time = 0.216595, size = 200, normalized size = 1.75 \[ \frac{1}{12} \, B b^{5} x^{12} + \frac{5}{9} \, B a b^{4} x^{9} + \frac{1}{9} \, A b^{5} x^{9} + \frac{5}{3} \, B a^{2} b^{3} x^{6} + \frac{5}{6} \, A a b^{4} x^{6} + \frac{10}{3} \, B a^{3} b^{2} x^{3} + \frac{10}{3} \, A a^{2} b^{3} x^{3} + 5 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )}{\rm ln}\left ({\left | x \right |}\right ) - \frac{15 \, B a^{4} b x^{6} + 30 \, A a^{3} b^{2} x^{6} + 2 \, B a^{5} x^{3} + 10 \, A a^{4} b x^{3} + A a^{5}}{6 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^5/x^7,x, algorithm="giac")
[Out]