Optimal. Leaf size=110 \[ -\frac {a^5 A}{7 x^7}-\frac {a^4 (a B+5 A b)}{4 x^4}-\frac {5 a^3 b (a B+2 A b)}{x}+5 a^2 b^2 x^2 (a B+A b)+\frac {1}{8} b^4 x^8 (5 a B+A b)+a b^3 x^5 (2 a B+A b)+\frac {1}{11} b^5 B x^{11} \]
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Rubi [A] time = 0.07, antiderivative size = 110, 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} \[ 5 a^2 b^2 x^2 (a B+A b)-\frac {a^4 (a B+5 A b)}{4 x^4}-\frac {5 a^3 b (a B+2 A b)}{x}-\frac {a^5 A}{7 x^7}+\frac {1}{8} b^4 x^8 (5 a B+A b)+a b^3 x^5 (2 a B+A b)+\frac {1}{11} b^5 B x^{11} \]
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^8} \, dx &=\int \left (\frac {a^5 A}{x^8}+\frac {a^4 (5 A b+a B)}{x^5}+\frac {5 a^3 b (2 A b+a B)}{x^2}+10 a^2 b^2 (A b+a B) x+5 a b^3 (A b+2 a B) x^4+b^4 (A b+5 a B) x^7+b^5 B x^{10}\right ) \, dx\\ &=-\frac {a^5 A}{7 x^7}-\frac {a^4 (5 A b+a B)}{4 x^4}-\frac {5 a^3 b (2 A b+a B)}{x}+5 a^2 b^2 (A b+a B) x^2+a b^3 (A b+2 a B) x^5+\frac {1}{8} b^4 (A b+5 a B) x^8+\frac {1}{11} b^5 B x^{11}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 110, normalized size = 1.00 \[ -\frac {a^5 A}{7 x^7}-\frac {a^4 (a B+5 A b)}{4 x^4}-\frac {5 a^3 b (a B+2 A b)}{x}+5 a^2 b^2 x^2 (a B+A b)+\frac {1}{8} b^4 x^8 (5 a B+A b)+a b^3 x^5 (2 a B+A b)+\frac {1}{11} b^5 B x^{11} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.81, size = 121, normalized size = 1.10 \[ \frac {56 \, B b^{5} x^{18} + 77 \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 616 \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} + 3080 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} - 3080 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} - 88 \, A a^{5} - 154 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{616 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 127, normalized size = 1.15 \[ \frac {1}{11} \, B b^{5} x^{11} + \frac {5}{8} \, B a b^{4} x^{8} + \frac {1}{8} \, A b^{5} x^{8} + 2 \, B a^{2} b^{3} x^{5} + A a b^{4} x^{5} + 5 \, B a^{3} b^{2} x^{2} + 5 \, A a^{2} b^{3} x^{2} - \frac {140 \, B a^{4} b x^{6} + 280 \, A a^{3} b^{2} x^{6} + 7 \, B a^{5} x^{3} + 35 \, A a^{4} b x^{3} + 4 \, A a^{5}}{28 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 117, normalized size = 1.06 \[ \frac {B \,b^{5} x^{11}}{11}+\frac {A \,b^{5} x^{8}}{8}+\frac {5 B a \,b^{4} x^{8}}{8}+A a \,b^{4} x^{5}+2 B \,a^{2} b^{3} x^{5}+5 A \,a^{2} b^{3} x^{2}+5 B \,a^{3} b^{2} x^{2}-\frac {5 \left (2 A b +B a \right ) a^{3} b}{x}-\frac {\left (5 A b +B a \right ) a^{4}}{4 x^{4}}-\frac {A \,a^{5}}{7 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 121, normalized size = 1.10 \[ \frac {1}{11} \, B b^{5} x^{11} + \frac {1}{8} \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{8} + {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{5} + 5 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{2} - \frac {140 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} + 4 \, A a^{5} + 7 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{28 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.34, size = 113, normalized size = 1.03 \[ x^8\,\left (\frac {A\,b^5}{8}+\frac {5\,B\,a\,b^4}{8}\right )-\frac {\frac {A\,a^5}{7}+x^6\,\left (5\,B\,a^4\,b+10\,A\,a^3\,b^2\right )+x^3\,\left (\frac {B\,a^5}{4}+\frac {5\,A\,b\,a^4}{4}\right )}{x^7}+\frac {B\,b^5\,x^{11}}{11}+5\,a^2\,b^2\,x^2\,\left (A\,b+B\,a\right )+a\,b^3\,x^5\,\left (A\,b+2\,B\,a\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.12, size = 129, normalized size = 1.17 \[ \frac {B b^{5} x^{11}}{11} + x^{8} \left (\frac {A b^{5}}{8} + \frac {5 B a b^{4}}{8}\right ) + x^{5} \left (A a b^{4} + 2 B a^{2} b^{3}\right ) + x^{2} \left (5 A a^{2} b^{3} + 5 B a^{3} b^{2}\right ) + \frac {- 4 A a^{5} + x^{6} \left (- 280 A a^{3} b^{2} - 140 B a^{4} b\right ) + x^{3} \left (- 35 A a^{4} b - 7 B a^{5}\right )}{28 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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