Optimal. Leaf size=114 \[ -\frac{a^5 A}{12 x^{12}}-\frac{a^4 (a B+5 A b)}{9 x^9}-\frac{5 a^3 b (a B+2 A b)}{6 x^6}-\frac{10 a^2 b^2 (a B+A b)}{3 x^3}+\frac{1}{3} b^4 x^3 (5 a B+A b)+5 a b^3 \log (x) (2 a B+A b)+\frac{1}{6} b^5 B x^6 \]
[Out]
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Rubi [A] time = 0.300941, 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 \[ -\frac{a^5 A}{12 x^{12}}-\frac{a^4 (a B+5 A b)}{9 x^9}-\frac{5 a^3 b (a B+2 A b)}{6 x^6}-\frac{10 a^2 b^2 (a B+A b)}{3 x^3}+\frac{1}{3} b^4 x^3 (5 a B+A b)+5 a b^3 \log (x) (2 a B+A b)+\frac{1}{6} b^5 B x^6 \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^3)^5*(A + B*x^3))/x^13,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{A a^{5}}{12 x^{12}} + \frac{B b^{5} \int ^{x^{3}} x\, dx}{3} - \frac{a^{4} \left (5 A b + B a\right )}{9 x^{9}} - \frac{5 a^{3} b \left (2 A b + B a\right )}{6 x^{6}} - \frac{10 a^{2} b^{2} \left (A b + B a\right )}{3 x^{3}} + \frac{5 a b^{3} \left (A b + 2 B a\right ) \log{\left (x^{3} \right )}}{3} + \frac{b^{4} \left (A b + 5 B a\right ) \int ^{x^{3}} A\, dx}{3 A} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**5*(B*x**3+A)/x**13,x)
[Out]
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Mathematica [A] time = 0.0742297, size = 118, normalized size = 1.04 \[ -\frac{a^5 \left (3 A+4 B x^3\right )+10 a^4 b x^3 \left (2 A+3 B x^3\right )+60 a^3 b^2 x^6 \left (A+2 B x^3\right )+120 a^2 A b^3 x^9-180 a b^3 x^{12} \log (x) (2 a B+A b)-60 a b^4 B x^{15}-6 b^5 x^{15} \left (2 A+B x^3\right )}{36 x^{12}} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^3)^5*(A + B*x^3))/x^13,x]
[Out]
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Maple [A] time = 0.012, size = 124, normalized size = 1.1 \[{\frac{{b}^{5}B{x}^{6}}{6}}+{\frac{A{x}^{3}{b}^{5}}{3}}+{\frac{5\,B{x}^{3}a{b}^{4}}{3}}-{\frac{A{a}^{5}}{12\,{x}^{12}}}+5\,A\ln \left ( x \right ) a{b}^{4}+10\,B\ln \left ( x \right ){a}^{2}{b}^{3}-{\frac{5\,{a}^{3}{b}^{2}A}{3\,{x}^{6}}}-{\frac{5\,{a}^{4}bB}{6\,{x}^{6}}}-{\frac{5\,{a}^{4}bA}{9\,{x}^{9}}}-{\frac{{a}^{5}B}{9\,{x}^{9}}}-{\frac{10\,{a}^{2}{b}^{3}A}{3\,{x}^{3}}}-{\frac{10\,{a}^{3}{b}^{2}B}{3\,{x}^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^5*(B*x^3+A)/x^13,x)
[Out]
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Maxima [A] time = 1.52177, size = 166, normalized size = 1.46 \[ \frac{1}{6} \, B b^{5} x^{6} + \frac{1}{3} \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{3} + \frac{5}{3} \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} \log \left (x^{3}\right ) - \frac{120 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} + 30 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} + 3 \, A a^{5} + 4 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{36 \, x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^5/x^13,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.220489, size = 166, normalized size = 1.46 \[ \frac{6 \, B b^{5} x^{18} + 12 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 180 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} \log \left (x\right ) - 120 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} - 30 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} - 3 \, A a^{5} - 4 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{36 \, x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^5/x^13,x, algorithm="fricas")
[Out]
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Sympy [A] time = 24.3282, size = 124, normalized size = 1.09 \[ \frac{B b^{5} x^{6}}{6} + 5 a b^{3} \left (A b + 2 B a\right ) \log{\left (x \right )} + x^{3} \left (\frac{A b^{5}}{3} + \frac{5 B a b^{4}}{3}\right ) - \frac{3 A a^{5} + x^{9} \left (120 A a^{2} b^{3} + 120 B a^{3} b^{2}\right ) + x^{6} \left (60 A a^{3} b^{2} + 30 B a^{4} b\right ) + x^{3} \left (20 A a^{4} b + 4 B a^{5}\right )}{36 x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**5*(B*x**3+A)/x**13,x)
[Out]
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GIAC/XCAS [A] time = 0.219719, size = 201, normalized size = 1.76 \[ \frac{1}{6} \, B b^{5} x^{6} + \frac{5}{3} \, B a b^{4} x^{3} + \frac{1}{3} \, A b^{5} x^{3} + 5 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )}{\rm ln}\left ({\left | x \right |}\right ) - \frac{250 \, B a^{2} b^{3} x^{12} + 125 \, A a b^{4} x^{12} + 120 \, B a^{3} b^{2} x^{9} + 120 \, A a^{2} b^{3} x^{9} + 30 \, B a^{4} b x^{6} + 60 \, A a^{3} b^{2} x^{6} + 4 \, B a^{5} x^{3} + 20 \, A a^{4} b x^{3} + 3 \, A a^{5}}{36 \, x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^3 + A)*(b*x^3 + a)^5/x^13,x, algorithm="giac")
[Out]