Optimal. Leaf size=91 \[ -\frac{a^5 B}{15 x^{15}}-\frac{5 a^4 b B}{12 x^{12}}-\frac{10 a^3 b^2 B}{9 x^9}-\frac{5 a^2 b^3 B}{3 x^6}-\frac{A \left (a+b x^3\right )^6}{18 a x^{18}}-\frac{5 a b^4 B}{3 x^3}+b^5 B \log (x) \]
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Rubi [A] time = 0.156191, antiderivative size = 91, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.15 \[ -\frac{a^5 B}{15 x^{15}}-\frac{5 a^4 b B}{12 x^{12}}-\frac{10 a^3 b^2 B}{9 x^9}-\frac{5 a^2 b^3 B}{3 x^6}-\frac{A \left (a+b x^3\right )^6}{18 a x^{18}}-\frac{5 a b^4 B}{3 x^3}+b^5 B \log (x) \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^3)^5*(A + B*x^3))/x^19,x]
[Out]
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Rubi in Sympy [A] time = 20.1783, size = 95, normalized size = 1.04 \[ - \frac{A \left (a + b x^{3}\right )^{6}}{18 a x^{18}} - \frac{B a^{5}}{15 x^{15}} - \frac{5 B a^{4} b}{12 x^{12}} - \frac{10 B a^{3} b^{2}}{9 x^{9}} - \frac{5 B a^{2} b^{3}}{3 x^{6}} - \frac{5 B a b^{4}}{3 x^{3}} + \frac{B b^{5} \log{\left (x^{3} \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**5*(B*x**3+A)/x**19,x)
[Out]
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Mathematica [A] time = 0.079167, size = 121, normalized size = 1.33 \[ -\frac{2 a^5 \left (5 A+6 B x^3\right )+15 a^4 b x^3 \left (4 A+5 B x^3\right )+50 a^3 b^2 x^6 \left (3 A+4 B x^3\right )+100 a^2 b^3 x^9 \left (2 A+3 B x^3\right )+150 a b^4 x^{12} \left (A+2 B x^3\right )+60 A b^5 x^{15}-180 b^5 B x^{18} \log (x)}{180 x^{18}} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^3)^5*(A + B*x^3))/x^19,x]
[Out]
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Maple [A] time = 0.012, size = 124, normalized size = 1.4 \[ -{\frac{5\,{a}^{3}{b}^{2}A}{6\,{x}^{12}}}-{\frac{5\,{a}^{4}bB}{12\,{x}^{12}}}-{\frac{{a}^{4}bA}{3\,{x}^{15}}}-{\frac{{a}^{5}B}{15\,{x}^{15}}}+{b}^{5}B\ln \left ( x \right ) -{\frac{5\,a{b}^{4}A}{6\,{x}^{6}}}-{\frac{5\,{a}^{2}{b}^{3}B}{3\,{x}^{6}}}-{\frac{10\,{a}^{2}{b}^{3}A}{9\,{x}^{9}}}-{\frac{10\,{a}^{3}{b}^{2}B}{9\,{x}^{9}}}-{\frac{{b}^{5}A}{3\,{x}^{3}}}-{\frac{5\,a{b}^{4}B}{3\,{x}^{3}}}-{\frac{A{a}^{5}}{18\,{x}^{18}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^5*(B*x^3+A)/x^19,x)
[Out]
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Maxima [A] time = 1.43841, size = 166, normalized size = 1.82 \[ \frac{1}{3} \, B b^{5} \log \left (x^{3}\right ) - \frac{60 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 150 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} + 200 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} + 75 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} + 10 \, A a^{5} + 12 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{180 \, x^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^5/x^19,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.225584, size = 166, normalized size = 1.82 \[ \frac{180 \, B b^{5} x^{18} \log \left (x\right ) - 60 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} - 150 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} - 200 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} - 75 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} - 10 \, A a^{5} - 12 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{180 \, x^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^5/x^19,x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**5*(B*x**3+A)/x**19,x)
[Out]
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GIAC/XCAS [A] time = 0.214539, size = 184, normalized size = 2.02 \[ B b^{5}{\rm ln}\left ({\left | x \right |}\right ) - \frac{147 \, B b^{5} x^{18} + 300 \, B a b^{4} x^{15} + 60 \, A b^{5} x^{15} + 300 \, B a^{2} b^{3} x^{12} + 150 \, A a b^{4} x^{12} + 200 \, B a^{3} b^{2} x^{9} + 200 \, A a^{2} b^{3} x^{9} + 75 \, B a^{4} b x^{6} + 150 \, A a^{3} b^{2} x^{6} + 12 \, B a^{5} x^{3} + 60 \, A a^{4} b x^{3} + 10 \, A a^{5}}{180 \, x^{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^5/x^19,x, algorithm="giac")
[Out]