Optimal. Leaf size=113 \[ -\frac {a^5 A}{8 x^8}-\frac {a^4 (a B+5 A b)}{5 x^5}-\frac {5 a^3 b (a B+2 A b)}{2 x^2}+10 a^2 b^2 x (a B+A b)+\frac {1}{7} b^4 x^7 (5 a B+A b)+\frac {5}{4} a b^3 x^4 (2 a B+A b)+\frac {1}{10} b^5 B x^{10} \]
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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} \begin {gather*} 10 a^2 b^2 x (a B+A b)-\frac {5 a^3 b (a B+2 A b)}{2 x^2}-\frac {a^4 (a B+5 A b)}{5 x^5}-\frac {a^5 A}{8 x^8}+\frac {1}{7} b^4 x^7 (5 a B+A b)+\frac {5}{4} a b^3 x^4 (2 a B+A b)+\frac {1}{10} b^5 B x^{10} \end {gather*}
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^9} \, dx &=\int \left (10 a^2 b^2 (A b+a B)+\frac {a^5 A}{x^9}+\frac {a^4 (5 A b+a B)}{x^6}+\frac {5 a^3 b (2 A b+a B)}{x^3}+5 a b^3 (A b+2 a B) x^3+b^4 (A b+5 a B) x^6+b^5 B x^9\right ) \, dx\\ &=-\frac {a^5 A}{8 x^8}-\frac {a^4 (5 A b+a B)}{5 x^5}-\frac {5 a^3 b (2 A b+a B)}{2 x^2}+10 a^2 b^2 (A b+a B) x+\frac {5}{4} a b^3 (A b+2 a B) x^4+\frac {1}{7} b^4 (A b+5 a B) x^7+\frac {1}{10} b^5 B x^{10}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 113, normalized size = 1.00 \begin {gather*} -\frac {a^5 A}{8 x^8}-\frac {a^4 (a B+5 A b)}{5 x^5}-\frac {5 a^3 b (a B+2 A b)}{2 x^2}+10 a^2 b^2 x (a B+A b)+\frac {1}{7} b^4 x^7 (5 a B+A b)+\frac {5}{4} a b^3 x^4 (2 a B+A b)+\frac {1}{10} b^5 B x^{10} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (a+b x^3\right )^5 \left (A+B x^3\right )}{x^9} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.72, size = 121, normalized size = 1.07 \begin {gather*} \frac {28 \, B b^{5} x^{18} + 40 \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 350 \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} + 2800 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} - 700 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} - 35 \, A a^{5} - 56 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{280 \, x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 124, normalized size = 1.10 \begin {gather*} \frac {1}{10} \, B b^{5} x^{10} + \frac {5}{7} \, B a b^{4} x^{7} + \frac {1}{7} \, A b^{5} x^{7} + \frac {5}{2} \, B a^{2} b^{3} x^{4} + \frac {5}{4} \, A a b^{4} x^{4} + 10 \, B a^{3} b^{2} x + 10 \, A a^{2} b^{3} x - \frac {100 \, B a^{4} b x^{6} + 200 \, A a^{3} b^{2} x^{6} + 8 \, B a^{5} x^{3} + 40 \, A a^{4} b x^{3} + 5 \, A a^{5}}{40 \, x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 114, normalized size = 1.01 \begin {gather*} \frac {B \,b^{5} x^{10}}{10}+\frac {A \,b^{5} x^{7}}{7}+\frac {5 B a \,b^{4} x^{7}}{7}+\frac {5 A a \,b^{4} x^{4}}{4}+\frac {5 B \,a^{2} b^{3} x^{4}}{2}+10 A \,a^{2} b^{3} x +10 B \,a^{3} b^{2} x -\frac {5 \left (2 A b +B a \right ) a^{3} b}{2 x^{2}}-\frac {\left (5 A b +B a \right ) a^{4}}{5 x^{5}}-\frac {A \,a^{5}}{8 x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 120, normalized size = 1.06 \begin {gather*} \frac {1}{10} \, B b^{5} x^{10} + \frac {1}{7} \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{7} + \frac {5}{4} \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{4} + 10 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x - \frac {100 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} + 5 \, A a^{5} + 8 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{40 \, x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 111, normalized size = 0.98 \begin {gather*} x^7\,\left (\frac {A\,b^5}{7}+\frac {5\,B\,a\,b^4}{7}\right )-\frac {\frac {A\,a^5}{8}+x^6\,\left (\frac {5\,B\,a^4\,b}{2}+5\,A\,a^3\,b^2\right )+x^3\,\left (\frac {B\,a^5}{5}+A\,b\,a^4\right )}{x^8}+\frac {B\,b^5\,x^{10}}{10}+10\,a^2\,b^2\,x\,\left (A\,b+B\,a\right )+\frac {5\,a\,b^3\,x^4\,\left (A\,b+2\,B\,a\right )}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.21, size = 133, normalized size = 1.18 \begin {gather*} \frac {B b^{5} x^{10}}{10} + x^{7} \left (\frac {A b^{5}}{7} + \frac {5 B a b^{4}}{7}\right ) + x^{4} \left (\frac {5 A a b^{4}}{4} + \frac {5 B a^{2} b^{3}}{2}\right ) + x \left (10 A a^{2} b^{3} + 10 B a^{3} b^{2}\right ) + \frac {- 5 A a^{5} + x^{6} \left (- 200 A a^{3} b^{2} - 100 B a^{4} b\right ) + x^{3} \left (- 40 A a^{4} b - 8 B a^{5}\right )}{40 x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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