Optimal. Leaf size=113 \[ \frac{5}{3} a^2 b^2 x^6 (a B+A b)+\frac{5}{3} a^3 b x^3 (a B+2 A b)+a^4 \log (x) (a B+5 A b)-\frac{a^5 A}{3 x^3}+\frac{1}{12} b^4 x^{12} (5 a B+A b)+\frac{5}{9} a b^3 x^9 (2 a B+A b)+\frac{1}{15} b^5 B x^{15} \]
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Rubi [A] time = 0.117054, antiderivative size = 113, 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, Rules used = {446, 76} \[ \frac{5}{3} a^2 b^2 x^6 (a B+A b)+\frac{5}{3} a^3 b x^3 (a B+2 A b)+a^4 \log (x) (a B+5 A b)-\frac{a^5 A}{3 x^3}+\frac{1}{12} b^4 x^{12} (5 a B+A b)+\frac{5}{9} a b^3 x^9 (2 a B+A b)+\frac{1}{15} b^5 B x^{15} \]
Antiderivative was successfully verified.
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Rule 446
Rule 76
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^5 \left (A+B x^3\right )}{x^4} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{(a+b x)^5 (A+B x)}{x^2} \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (5 a^3 b (2 A b+a B)+\frac{a^5 A}{x^2}+\frac{a^4 (5 A b+a B)}{x}+10 a^2 b^2 (A b+a B) x+5 a b^3 (A b+2 a B) x^2+b^4 (A b+5 a B) x^3+b^5 B x^4\right ) \, dx,x,x^3\right )\\ &=-\frac{a^5 A}{3 x^3}+\frac{5}{3} a^3 b (2 A b+a B) x^3+\frac{5}{3} a^2 b^2 (A b+a B) x^6+\frac{5}{9} a b^3 (A b+2 a B) x^9+\frac{1}{12} b^4 (A b+5 a B) x^{12}+\frac{1}{15} b^5 B x^{15}+a^4 (5 A b+a B) \log (x)\\ \end{align*}
Mathematica [A] time = 0.0394044, size = 115, normalized size = 1.02 \[ \frac{5}{3} a^2 b^2 x^6 (a B+A b)+\frac{5}{3} a^3 b x^3 (a B+2 A b)+\log (x) \left (5 a^4 A b+a^5 B\right )-\frac{a^5 A}{3 x^3}+\frac{1}{12} b^4 x^{12} (5 a B+A b)+\frac{5}{9} a b^3 x^9 (2 a B+A b)+\frac{1}{15} b^5 B x^{15} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 123, normalized size = 1.1 \begin{align*}{\frac{{b}^{5}B{x}^{15}}{15}}+{\frac{A{x}^{12}{b}^{5}}{12}}+{\frac{5\,B{x}^{12}a{b}^{4}}{12}}+{\frac{5\,A{x}^{9}a{b}^{4}}{9}}+{\frac{10\,B{x}^{9}{a}^{2}{b}^{3}}{9}}+{\frac{5\,A{x}^{6}{a}^{2}{b}^{3}}{3}}+{\frac{5\,B{x}^{6}{a}^{3}{b}^{2}}{3}}+{\frac{10\,A{x}^{3}{a}^{3}{b}^{2}}{3}}+{\frac{5\,B{x}^{3}{a}^{4}b}{3}}-{\frac{A{a}^{5}}{3\,{x}^{3}}}+5\,A\ln \left ( x \right ){a}^{4}b+B\ln \left ( x \right ){a}^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.48549, size = 162, normalized size = 1.43 \begin{align*} \frac{1}{15} \, B b^{5} x^{15} + \frac{1}{12} \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{12} + \frac{5}{9} \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{9} + \frac{5}{3} \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{6} + \frac{5}{3} \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{3} - \frac{A a^{5}}{3 \, x^{3}} + \frac{1}{3} \,{\left (B a^{5} + 5 \, A a^{4} b\right )} \log \left (x^{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.47553, size = 281, normalized size = 2.49 \begin{align*} \frac{12 \, B b^{5} x^{18} + 15 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 100 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} + 300 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} + 300 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} - 60 \, A a^{5} + 180 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3} \log \left (x\right )}{180 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.506031, size = 133, normalized size = 1.18 \begin{align*} - \frac{A a^{5}}{3 x^{3}} + \frac{B b^{5} x^{15}}{15} + a^{4} \left (5 A b + B a\right ) \log{\left (x \right )} + x^{12} \left (\frac{A b^{5}}{12} + \frac{5 B a b^{4}}{12}\right ) + x^{9} \left (\frac{5 A a b^{4}}{9} + \frac{10 B a^{2} b^{3}}{9}\right ) + x^{6} \left (\frac{5 A a^{2} b^{3}}{3} + \frac{5 B a^{3} b^{2}}{3}\right ) + x^{3} \left (\frac{10 A a^{3} b^{2}}{3} + \frac{5 B a^{4} b}{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.22758, size = 193, normalized size = 1.71 \begin{align*} \frac{1}{15} \, B b^{5} x^{15} + \frac{5}{12} \, B a b^{4} x^{12} + \frac{1}{12} \, A b^{5} x^{12} + \frac{10}{9} \, B a^{2} b^{3} x^{9} + \frac{5}{9} \, A a b^{4} x^{9} + \frac{5}{3} \, B a^{3} b^{2} x^{6} + \frac{5}{3} \, A a^{2} b^{3} x^{6} + \frac{5}{3} \, B a^{4} b x^{3} + \frac{10}{3} \, A a^{3} b^{2} x^{3} +{\left (B a^{5} + 5 \, A a^{4} b\right )} \log \left ({\left | x \right |}\right ) - \frac{B a^{5} x^{3} + 5 \, A a^{4} b x^{3} + A a^{5}}{3 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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