Optimal. Leaf size=113 \[ -\frac {a^5 A}{5 x^5}-\frac {a^4 (a B+5 A b)}{2 x^2}+5 a^3 b x (a B+2 A b)+\frac {5}{2} a^2 b^2 x^4 (a B+A b)+\frac {1}{10} b^4 x^{10} (5 a B+A b)+\frac {5}{7} a b^3 x^7 (2 a B+A b)+\frac {1}{13} b^5 B x^{13} \]
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Rubi [A] time = 0.06, antiderivative size = 113, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {448} \[ \frac {5}{2} a^2 b^2 x^4 (a B+A b)-\frac {a^4 (a B+5 A b)}{2 x^2}+5 a^3 b x (a B+2 A b)-\frac {a^5 A}{5 x^5}+\frac {1}{10} b^4 x^{10} (5 a B+A b)+\frac {5}{7} a b^3 x^7 (2 a B+A b)+\frac {1}{13} b^5 B x^{13} \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^5 \left (A+B x^3\right )}{x^6} \, dx &=\int \left (5 a^3 b (2 A b+a B)+\frac {a^5 A}{x^6}+\frac {a^4 (5 A b+a B)}{x^3}+10 a^2 b^2 (A b+a B) x^3+5 a b^3 (A b+2 a B) x^6+b^4 (A b+5 a B) x^9+b^5 B x^{12}\right ) \, dx\\ &=-\frac {a^5 A}{5 x^5}-\frac {a^4 (5 A b+a B)}{2 x^2}+5 a^3 b (2 A b+a B) x+\frac {5}{2} a^2 b^2 (A b+a B) x^4+\frac {5}{7} a b^3 (A b+2 a B) x^7+\frac {1}{10} b^4 (A b+5 a B) x^{10}+\frac {1}{13} b^5 B x^{13}\\ \end {align*}
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Mathematica [A] time = 0.06, size = 113, normalized size = 1.00 \[ -\frac {a^5 A}{5 x^5}-\frac {a^4 (a B+5 A b)}{2 x^2}+5 a^3 b x (a B+2 A b)+\frac {5}{2} a^2 b^2 x^4 (a B+A b)+\frac {1}{10} b^4 x^{10} (5 a B+A b)+\frac {5}{7} a b^3 x^7 (2 a B+A b)+\frac {1}{13} b^5 B x^{13} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.17, size = 121, normalized size = 1.07 \[ \frac {70 \, B b^{5} x^{18} + 91 \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 650 \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} + 2275 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} + 4550 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} - 182 \, A a^{5} - 455 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{910 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 124, normalized size = 1.10 \[ \frac {1}{13} \, B b^{5} x^{13} + \frac {1}{2} \, B a b^{4} x^{10} + \frac {1}{10} \, A b^{5} x^{10} + \frac {10}{7} \, B a^{2} b^{3} x^{7} + \frac {5}{7} \, A a b^{4} x^{7} + \frac {5}{2} \, B a^{3} b^{2} x^{4} + \frac {5}{2} \, A a^{2} b^{3} x^{4} + 5 \, B a^{4} b x + 10 \, A a^{3} b^{2} x - \frac {5 \, B a^{5} x^{3} + 25 \, A a^{4} b x^{3} + 2 \, A a^{5}}{10 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 119, normalized size = 1.05 \[ \frac {B \,b^{5} x^{13}}{13}+\frac {A \,b^{5} x^{10}}{10}+\frac {B a \,b^{4} x^{10}}{2}+\frac {5 A a \,b^{4} x^{7}}{7}+\frac {10 B \,a^{2} b^{3} x^{7}}{7}+\frac {5 A \,a^{2} b^{3} x^{4}}{2}+\frac {5 B \,a^{3} b^{2} x^{4}}{2}+10 A \,a^{3} b^{2} x +5 B \,a^{4} b x -\frac {\left (5 A b +B a \right ) a^{4}}{2 x^{2}}-\frac {A \,a^{5}}{5 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.73, size = 120, normalized size = 1.06 \[ \frac {1}{13} \, B b^{5} x^{13} + \frac {1}{10} \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{10} + \frac {5}{7} \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{7} + \frac {5}{2} \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{4} + 5 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x - \frac {2 \, A a^{5} + 5 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{10 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 108, normalized size = 0.96 \[ x^{10}\,\left (\frac {A\,b^5}{10}+\frac {B\,a\,b^4}{2}\right )-\frac {\frac {A\,a^5}{5}+x^3\,\left (\frac {B\,a^5}{2}+\frac {5\,A\,b\,a^4}{2}\right )}{x^5}+\frac {B\,b^5\,x^{13}}{13}+\frac {5\,a^2\,b^2\,x^4\,\left (A\,b+B\,a\right )}{2}+5\,a^3\,b\,x\,\left (2\,A\,b+B\,a\right )+\frac {5\,a\,b^3\,x^7\,\left (A\,b+2\,B\,a\right )}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.48, size = 133, normalized size = 1.18 \[ \frac {B b^{5} x^{13}}{13} + x^{10} \left (\frac {A b^{5}}{10} + \frac {B a b^{4}}{2}\right ) + x^{7} \left (\frac {5 A a b^{4}}{7} + \frac {10 B a^{2} b^{3}}{7}\right ) + x^{4} \left (\frac {5 A a^{2} b^{3}}{2} + \frac {5 B a^{3} b^{2}}{2}\right ) + x \left (10 A a^{3} b^{2} + 5 B a^{4} b\right ) + \frac {- 2 A a^{5} + x^{3} \left (- 25 A a^{4} b - 5 B a^{5}\right )}{10 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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